Lets keep it real basic.

Picture a soapy sponge.  Put it in a sink of clean water.  Push down on it, the soap squeezes out.  when your hand is taken off, clean water is sucked in.  Do this a number of times and eventually you have a clean sponge.

Now lets look at muscle.  I don't care what kind of athlete you happen to be, competitive, recreational, or industrial, if you're alive you're using muscles.  Various toxins accumulate, muscles tighten restricting blood flow, which in turn causes aches and pains or, worse yet, injury.

Massage releases the build up in the muscles much like pressing on the sponge.  The pressure on the muscle moves the toxins out, and when the pressure is released, fresh blood moves into the muscle.

With the toxic 'dams' removed, blood can flow freely.  With the fullest flow of blood available, many muscle "by products", such as Lactic Acid and so on, are whisked away in the newly opened river.  This free flow allows fresh nutrients and "oxygen-rich" blood to flood the area.  This is necessary for the muscle to be at its fullest potential.