"Rooting for" means cheering something/someone on; to wish success for them. Unlike actually cheering them on, rooting for them can be done silently or aloud. It's mainly used in the USA in reference to sports, you "root for your hometeam," for example. I have NO IDEA how that got started, but it seems to mainly only be said in America.
Just never say it to an Australian / New Zealander . . . they use the term "root someone" as sexual slang, lol.
