Imply and infer are opposites, like a throw and a catch. To imply is to hint at something, but to infer is to make an educated guess. The speaker does the implying, and the listener does the inferring.

To imply is to suggest something indirectly. If you hand your friend a stack of napkins during dinner, you imply that she needs them. Things can imply, too, like a chimney that implies a fireplace. Check out these examples:

By their very definition, flea markets imply cheap prices for used and unwanted items, as is still the case in most other places. (New York Times) Stern also implied the entire season might be at risk. (Seattle Times) It isn't fair to imply that cardiovascular disease is going away. (Nature)

Infer is on the receiving end of imply, yet infer is often used to mean imply. To infer is to gather, deduce, or figure out.Writers tend to know how to use infer correctly:

He talks about having led in the private sector but voters have to infer too much about what that means. (Slate) They were also better at inferring feelings from images of just the eyes. (Scientific American) Yet it must not be inferred that farming women are without mental ability or common sense. (Sidney Lewis Gulick)

Like baseball? Theodore Bernstein, in his classic The Careful Writer, gives us a way to keep imply and infer straight: "The implier is the pitcher; the inferrer is the catcher."