Must I back up my data before installing a second OS? What will happen if I don't back it up?
Something may go wrong, either due to a bug in the Ubuntu installer or you making a mistake. The Ubuntu installer has full access to your disk and is capable of destroying everything. The programmers from Canonical have used a lot of time to design an installer that won't do this unless you explicitly ask it to, but they cannot take responsibility if some mistake slipped through anyway.
In other words, making a backup is for the sake of "better safe than sorry".