It's the first thing you hear when the action starts. It pumps you up. It sets the initial mood. Platformers, beat 'em ups, racing, arcade, console... it spans a wide variety.
It's nearly its own subgenre of music.
Here are some examples (I'll leave out the obvious ones, like Green Hill Zone, Corneria, etc.)
Knights of the Round is a perfect example of that excitement & adrenaline administered at the start of the game.
Although not my favorite of the series,
Double Dragon 3 had a certain aesthetic value to it, thanks in part to the music (not composed by Kazunaka Yamane in this one).
Everything in
Last Blade was beautiful. I don't remember if this music was
always played first, though.
Some are more relaxed, in
Mega Man 8's case, likely to emphasize the ill-fated present with the eeriness of the past (notice the destroyed Mecha Dragon in the background).
Looking back at
Wave Race 64, I can't remember how I managed to stand that announcer.
What's your favorite starting stage theme?