Imply vs Infer

The English verbs imply and infer are often confused by English speakers. That’s not to imply that you’re one of them, but if that’s how you infer it, go ahead and read this lesson.

A. Imply
To imply means to suggest or to express something indirectly, rather than just coming out and saying it plainly:

I don’t mean to imply that you’re doing something wrong, but…
The expression on your face implies that you don’t believe me.
He didn’t say it in so many words, but he implied that we were required to "volunteer."
What are you implying?

The noun is implication.

There was a strong implication that attendance was required.

(There’s also an unrelated meaning of involvement: His implication in the theft is grounds for dismissal.)

B. Infer
To infer means to read meaning into what was just said, to draw a conclusion from something that was not specifically stated:

From that, I infer that you think I’m doing something wrong.
Am I meant to infer that you don’t believe me?
He didn’t say it in so many words, but I inferred that we were required to "volunteer."
I don’t know what to infer from that.

The noun is inference.
We have many inferences but no real facts.

Source:
http://www.elearnenglishlanguage.com/blog/english-mistakes/imply-vs-infer/