If you use iTunes on your computer to download a song, it will be on your computer and not on your iPad. Syncing copies the song from your computer to the iPad so it will be in both places.
If you download a song from the iTunes store using your iPad, the tune will be on your iPad and not on your computer. You have the option of backing it up (syncing it) to your computer so you don't have to download it again from the net should it get erased from your iPad somehow.
Syncing can be done either through a USB cable connected between your iPad and your computer while running the iTunes program, or it can be done via WiFi. The WiFi backups happen silently in the background. You don't have to do anything.
If for some reason you don't want your music backed up to your computer via WiFi, then don't check the button. Offhand, I can't think of any reason that you wouldn't want this.