Known as the boxing muscle because it allows your scapula (shoulder blade) to protract (come forward around the body by moving anterior and lateral) so that you can throw a punch.  Did you realize your shoulder blade has to move in order for you to get full range of motion out of your arm?
The serratus is also highly responsible for keeping the scapular flat against the rib cage and preventing winging (when the inside edge (medial border) of the shoulder blade sticks out).  Next time you’re at the gym watch someone do a push up.  If you can see their scapula pull away from the ribs and spine they aren’t using their serratus and they aren’t doing pushups properly.
If the shoulder blade does rest where it is supposed, against your ribs, it can cause pain, discomfort and reduce the range of motion in your shoulder.
The serratus connects to the medial border of the scapula, wraps underneath it along the ribs and connects to the first eight or nine rips on the side of the body, under the arm.  It wraps around the ribs like fingers holding each rib in place.   Since it touches the ribs, in addition to helping  hold the scapula in place, it helps aid in breathing.  Take a take breath and sigh when you release it—your serratus at work (at least in part).
Want to feel it?  Lay your left hand along the ribs under your right armpit.  Now feel you armpit get heavy like you are pulling down on it.  The muscle that pops up under your hand is your serratus.  Try it on the other side.
The serratus is one of my favorite muscles.  Maybe you’ll think about it a little more next time you throw a punch in boxing or kick boxing class, while doing a pushup or when you put on a backless dress.