I think the commonly accepted theory is that your brain is sorting through the day, through problems, through life. Even just playing. This makes sense seeing as how quickly humans fall apart without sleep.

I was so tired once, that all I could hear was The Spice Girls Wannabe, and just the chorus because I never actually listened to their music, just the repetition of:

YO, I’ᒪᒪ TEᒪᒪ YOᑌ ᗯᕼᗩT I ᗯᗩᑎT ᗯᕼᗩT I ᖇEᗩᒪᒪY, ᖇEᗩᒪᒪY ᗯᗩᑎT
SO TEᒪᒪ ᗰE ᗯᕼᗩT YOᑌ ᗯᗩᑎT, ᗯᕼᗩT YOᑌ ᖇEᗩᒪᒪY, ᖇEᗩᒪᒪY ᗯᗩᑎT