It started with the terrible towel in football for the Steelers, then it moved on to other sports. Why at different times though? Various reasons, it could be that they found something in the game exciting, or they're trying to get someones attention, etc. I really couldn't tell you why they're different colors, some times it just depends on the teams!
When your at any sports event, their are big jumbo trons(tv's kinda)that say stuff like make some noise, clap, etc.at baseball games they say swing your towels so everybody does it. You can't see it on tv but you can see the jumbotrons if you go their in person