The desktop environment (DE) is what makes up most of the user interface. It may include system panels, docks, window borders, backgrounds, and desktop widgets, among other things. GNU/Linux has a wide variety of DEs avaliable—this page will outline some of the most popular ones.
It is important to note that no DE is tied to a particular GNU/Linux distribution, or vice versa. Thus, if your distribution of choice is Debian, you may use GNOME, or KDE, or both GNOME and KDE (if you installed both). You can install as many different DEs as you want and try them all!
Computers in the LUG@UCLA Lounge have many DEs installed for you to try at your own leisure.
GNOME is touch-friendly desktop environment that aims to be simple to use while also offering a full set of features that appeal to advanced users. If it appears to be missing a feature, you can probably find something interesting in the GNOME Shell Extensions database.
Distributions that come with GNOME: