In strength training, concentric motion means the muscle or muscle group we are addressing is shortening, and eccentric means it is contracting while lengthening, under control. Of course, whenever one muscle contracts, its opposing muscle must lengthen. It's complicated, though, because during controlled effort neither relaxes.
Getting stronger entails breaking down muscle so it can regrow stronger and it seems as if the eccentric motion does a better job of that than the concentric although the latter tends to be where we feel we are working hardest. In the simplest example, when you do a barbell squat the squatting requires eccentric contraction for your quads and glutes, and the stand-up is concentric for them. Vice versa for the hamstrings. That's why your trainer may demand that, in a curl or bench press, for examples, you lower the weight to a count of 5 or 10 instead of letting gravity do more of the work. Some people call that "negative" training, or just say "control it down."
Strength training offers a fun chance to brush up on your human anatomy. While most powerlifts engage the entire body to some extent (which is why they are efficient strength-training tools, like the deadlift), generally most of the work is done by specific muscle groups. Let's consider the bench press, which is designed to not be a full-body exertion but instead to isolate upper body muscles - chest, upper back, shoulders, and arms. The concentric and eccentric contractions of the bench are explained well here. You can see why your biceps get pumped during bench even though pecs and triceps do the lifting - the control down is an eccentric move for the triceps and pecs but concentric/stabilizing for the biceps. After all, you can't drop that barbell.
The only place I can think of where you let gravity do most of the work is in the deadlift where the control-down is less important. You can almost let the bar drop.
Fitness Defined: Concentric and Eccentric Contractions (and Why It Matters)
Lowering weight during resistance training may make you stronger than the lifting
How to pack on muscle with eccentric exercise - Eccentric training has lots of perks—and it’s easy to work it into your routine.
