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).
When youre busy in the kitchen, its very easy to accidentally touch a burner, which can cause minor to serious burns. This risk is especially great for children, who can reach up onto the stove without being able to see the heat source. Since the induction cooker elements never get hot, accidental contact during cooking will not cause injury.