To imply something means to suggest it in an indirect way, without saying it directly.
To infer something is to form a conclusion from the information available (especially if the information available does not state things directly):
These two words describe the same event but from the two different sides (similar to lend and borrow). The speaker or writer implies a point (suggests it indirectly). The reader or listener infers a point (comes to their own conclusion after considering the indirect information).