Both imply and infer are
Both verbs have to do with the communication of information.
The difference between the two is that imply refers to giving information, while infer refers to receiving information.
Imply means to strongly suggest the truth or existence of something that is not expressly stated.
The speaker, or someone who is giving information, may imply something.
Infer means to deduce or conclude information from evidence and reasoning rather than from explicit statement of that information.
The listener, or someone who is receiving information, may infer something.
The following examples clearly show the difference between the two words:
One who gives information implies.
One who receives information infers.
Link to exercises on imply / infer.