I assume you know what 3D printing is. It is rapid prototyping for objects. FPGAs are rapid prototyping for processors.

Oversimplified, a processor contains logic gates and wires between them. While there are many kinds of logic gates, there is a rule that from one specific type and lots of wires, you can build any kind of processor, or logic circuit. From this follows, that not the logic gate is what matters, but how you compose them, alas the wires.

An FPGA contains loads of this one logic gate. Think of a gate array. Remember, it's called Field-Programmable Gate Array! As for the wires, FPGAs don't contain fixed wires, but a mechanism to dynamically define how those logic gates are connected. That configuration can be loaded onto the FPGA, in form of a configuration file. You can even change it later. That's called programming the FPGA. So by now we have covered 75% of the name, programmable gate arrays. Field-Programmable simply means, that the wiring is not defined (programmed) in the factory, when the processor is manufactured, rather, it is defined in the field.

Let it sink into your brain, because these few words will soon change the world: Field-Programmable Gate Arrays. Now, they kind of make sense, don't they? :)

If you want to know more, drop by at Wikipedia: Field-programmable gate array.