The "eccentric" phase of muscle action is generally when you are lowering the resistance against gravity. When you are doing the seated shoulder press, for example, the upward motion is concentric (muscle fibers contracting). And eccentric (when the muscle fibers are resisting the lowering speed of the resistance.
The eccentric phase of muscle contraction is often misunderstood. Some research tells us that of the two directions of muscle contraction (eccentric and concentric), the eccentric phase is most important for muscular development.
There is a third action of muscle contraction called "static contraction." It's a little confusing because when a muscle group is in static contraction, there is no movement. The resistance is moved through the range of motion (ROM) and stopped at some place in that range. An would be example doing an dumbbell (DB) arm curl and stopping the motion with the forearm is parallel with the deck.
I recommend 95% of your exercises go through the full range of motion (ROM), with a slower eccentric phase than the concentric phase. About a 2-to-1 time ratio is a good; 3-to-1 is better. In other words, curl up to a two-second count, but lower at three-seconds.
Remember, in general, to exhale on the concentric and inhale on the eccentric. Don't hold your breath. Obviously when you are doing a unilateral exercise (one side of the body at a time such as DB curls), you will just breath however feels comfortable.