1. To come very close to failing at something but succeed in the end. That marathon was so exhausting, I barely made it! I barely made it through math class this semester.

2. To come very close to being late for something, such as a deadline, appointment, class, etc., but manage to arrive on time in the end. A shortening of "barely make it on time." If you leave right now, you'll just barely make it to the film before it starts.