When you infer something, you're reading between the lines. Infer is the opposite of "imply." When you imply something, you send signals that someone else needs to infer.
When we infer, we're listening closely to someone and guessing at things they mean but haven't actually said. When we infer, we're guessing, but not making wild guesses. We're making deductions — guesses based on logic. Another kind of inferring is more scientific, like when a scientist has part of a dinosaur fossil and can infer what the rest of the dinosaur looked like. When you see the word infer, think "educated guess."