The difference between implying and inferring is this: an author who writes that all men are mortal and Socrates is a man implies that Socrates is mortal; a reader who is so subtle as to notice that the author implies that and to consciously think "Therefore Socrates is mortal" infers that Socrates is mortal.
In reading, inferences are made about parts of the text where the meaning is implied but not explicit. Assesments of the ability to make inferences about written text are used to measure reading skill.
This article is a stub. You can help Wikipedia by fixing it.