Here is an excerpt from Wikipedia that is related. It seems that there are many good articles there on what the muscles each do.
I believe that "elbow flexion" is the motion involved in a pool stroke.
Brachialis muscle
From Wikipedia, the free encyclopedia
Actions flexion at elbow joint
Latin musculus brachialis
The brachialis (brachialis anticus) is a muscle in the upper arm that flexes the elbow joint. It lies deeper than the biceps brachii, and makes up part of the floor of the region known as the cubital fossa. The brachialis is the prime mover of elbow flexion. While the biceps brachii appears as a large anterior bulge on the arm and commands considerable interest among body builders, the brachialis underlying it actually generates about 50% more power and is thus the prime mover of elbow flexion.[1]