To imply something means to suggest it in an indirect way, without saying it directly.
Larry's remarks implied that he'd be leaving the company soon.
The evidence seems to imply that the suspect is innocent of the crime.
To infer something is to form a conclusion from the information available (especially if the information available does not state things directly):
From Larry's remarks, I inferred that he'd probably be leaving the company soon.
Based on the evidence, the judge inferred that the suspect was innocent.
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).
If you are carrying excess weight and it wonít budge, it may be because you now need fewer calories. Over 50s who arenít active need 200 fewer calories per day than those who lead a very physically active life. Adjust your diet to accommodate your slowing metabolism, for example, by reducing portion size rather than by cutting out foods.