I will just give the analogy with which I understand memory consistency models (or memory models, for short). It is inspired by Leslie Lamport's seminal paper "Time, Clocks, and the Ordering of Events in a Distributed System". The analogy is apt and has fundamental significance, but may be overkill for many people. However, I hope it provides a mental image (a pictorial representation) that facilitates reasoning about memory consistency models.

Let’s view the histories of all memory locations in a space-time diagram in which the horizontal axis represents the address space (i.e., each memory location is represented by a point on that axis) and the vertical axis represents time (we will see that, in general, there is not a universal notion of time). The history of values held by each memory location is, therefore, represented by a vertical column at that memory address. Each value change is due to one of the threads writing a new value to that location. By a memory image, we will mean the aggregate/combination of values of all memory locations observable at a particular time by a particular thread.

Quoting from "A Primer on Memory Consistency and Cache Coherence"

The intuitive (and most restrictive) memory model is sequential consistency (SC) in which a multithreaded execution should look like an interleaving of the sequential executions of each constituent thread, as if the threads were time-multiplexed on a single-core processor.

That global memory order can vary from one run of the program to another and may not be known beforehand. The characteristic feature of SC is the set of horizontal slices in the address-space-time diagram representing planes of simultaneity (i.e., memory images). On a given plane, all of its events (or memory values) are simultaneous. There is a notion of Absolute Time, in which all threads agree on which memory values are simultaneous. In SC, at every time instant, there is only one memory image shared by all threads. That's, at every instant of time, all processors agree on the memory image (i.e., the aggregate content of memory). Not only does this imply that all threads view the same sequence of values for all memory locations, but also that all processors observe the same combinations of values of all variables. This is the same as saying all memory operations (on all memory locations) are observed in the same total order by all threads.

In relaxed memory models, each thread will slice up address-space-time in its own way, the only restriction being that slices of each thread shall not cross each other because all threads must agree on the history of every individual memory location (of course, slices of different threads may, and will, cross each other). There is no universal way to slice it up (no privileged foliation of address-space-time). Slices do not have to be planar (or linear). They can be curved and this is what can make a thread read values written by another thread out of the order they were written in. Histories of different memory locations may slide (or get stretched) arbitrarily relative to each other when viewed by any particular thread. Each thread will have a different sense of which events (or, equivalently, memory values) are simultaneous. The set of events (or memory values) that are simultaneous to one thread are not simultaneous to another. Thus, in a relaxed memory model, all threads still observe the same history (i.e., sequence of values) for each memory location. But they may observe different memory images (i.e., combinations of values of all memory locations). Even if two different memory locations are written by the same thread in sequence, the two newly written values may be observed in different order by other threads.

[Picture from Wikipedia]

Readers familiar with Einstein’s Special Theory of Relativity will notice what I am alluding to. Translating Minkowski’s words into the memory models realm: address space and time are shadows of address-space-time. In this case, each observer (i.e., thread) will project shadows of events (i.e., memory stores/loads) onto his own world-line (i.e., his time axis) and his own plane of simultaneity (his address-space axis). Threads in the C++11 memory model correspond to observers that are moving relative to each other in special relativity. Sequential consistency corresponds to the Galilean space-time (i.e., all observers agree on one absolute order of events and a global sense of simultaneity).

The resemblance between memory models and special relativity stems from the fact that both define a partially-ordered set of events, often called a causal set. Some events (i.e., memory stores) can affect (but not be affected by) other events. A C++11 thread (or observer in physics) is no more than a chain (i.e., a totally ordered set) of events (e.g., memory loads and stores to possibly different addresses).

In relativity, some order is restored to the seemingly chaotic picture of partially ordered events, since the only temporal ordering that all observers agree on is the ordering among “timelike” events (i.e., those events that are in principle connectible by any particle going slower than the speed of light in a vacuum). Only the timelike related events are invariantly ordered. Time in Physics, Craig Callender.

In C++11 memory model, a similar mechanism (the acquire-release consistency model) is used to establish these local causality relations.

To provide a definition of memory consistency and a motivation for abandoning SC, I will quote from "A Primer on Memory Consistency and Cache Coherence"

For a shared memory machine, the memory consistency model defines the architecturally visible behavior of its memory system. The correctness criterion for a single processor core partitions behavior between “one correct result” and “many incorrect alternatives”. This is because the processor’s architecture mandates that the execution of a thread transforms a given input state into a single well-defined output state, even on an out-of-order core. Shared memory consistency models, however, concern the loads and stores of multiple threads and usually allow many correct executions while disallowing many (more) incorrect ones. The possibility of multiple correct executions is due to the ISA allowing multiple threads to execute concurrently, often with many possible legal interleavings of instructions from different threads. Relaxed or weak memory consistency models are motivated by the fact that most memory orderings in strong models are unnecessary. If a thread updates ten data items and then a synchronization flag, programmers usually do not care if the data items are updated in order with respect to each other but only that all data items are updated before the flag is updated (usually implemented using FENCE instructions). Relaxed models seek to capture this increased ordering flexibility and preserve only the orders that programmers “require” to get both higher performance and correctness of SC. For example, in certain architectures, FIFO write buffers are used by each core to hold the results of committed (retired) stores before writing the results to the caches. This optimization enhances performance but violates SC. The write buffer hides the latency of servicing a store miss. Because stores are common, being able to avoid stalling on most of them is an important benefit. For a single-core processor, a write buffer can be made architecturally invisible by ensuring that a load to address A returns the value of the most recent store to A even if one or more stores to A are in the write buffer. This is typically done by either bypassing the value of the most recent store to A to the load from A, where “most recent” is determined by program order, or by stalling a load of A if a store to A is in the write buffer. When multiple cores are used, each will have its own bypassing write buffer. Without write buffers, the hardware is SC, but with write buffers, it is not, making write buffers architecturally visible in a multicore processor. Store-store reordering may happen if a core has a non-FIFO write buffer that lets stores depart in a different order than the order in which they entered. This might occur if the first store misses in the cache while the second hits or if the second store can coalesce with an earlier store (i.e., before the first store). Load-load reordering may also happen on dynamically-scheduled cores that execute instructions out of program order. That can behave the same as reordering stores on another core (Can you come up with an example interleaving between two threads?). Reordering an earlier load with a later store (a load-store reordering) can cause many incorrect behaviors, such as loading a value after releasing the lock that protects it (if the store is the unlock operation). Note that store-load reorderings may also arise due to local bypassing in the commonly implemented FIFO write buffer, even with a core that executes all instructions in program order.

Because cache coherence and memory consistency are sometimes confused, it is instructive to also have this quote:

Unlike consistency, cache coherence is neither visible to software nor required. Coherence seeks to make the caches of a shared-memory system as functionally invisible as the caches in a single-core system. Correct coherence ensures that a programmer cannot determine whether and where a system has caches by analyzing the results of loads and stores. This is because correct coherence ensures that the caches never enable new or different functional behavior (programmers may still be able to infer likely cache structure using timing information). The main purpose of cache coherence protocols is maintaining the single-writer-multiple-readers (SWMR) invariant for every memory location. An important distinction between coherence and consistency is that coherence is specified on a per-memory location basis, whereas consistency is specified with respect to all memory locations.

Continuing with our mental picture, the SWMR invariant corresponds to the physical requirement that there be at most one particle located at any one location but there can be an unlimited number of observers of any location.