NOTE: If you are running TuneUp 3.0 or higher, this support item is no longer valid. All support documentation for 3.0 and higher can be found under TuneUp Support - Learn More.
Mac OS X 10.7 and above (otherwise known as Lion) provides a feature for applications called "Full-Screen Apps" whereby applications can take up the entire screen space. Since TuneUp is meant to be a companion application to iTunes, it does not support Full Screen mode.
If TuneUp is Attached to iTunes, and you choose to "Go Full Screen" with iTunes, TuneUp will move into the other "Space" just like any other App that happened to be open. If you "Go Back", TuneUp will re-attach to iTunes.