screen can do a lot of stuff, see?
screen can detach from the terminal. All of the programs running in screen will remain exactly as they are after a detach. This means that you can start a program and leave it running even though you log in and out several times. You can even go to a different computer, ssh to the one that's running screen and access your running programs remotely.
screen can multiplex a terminal. Within a single screen session, you can have multiple screen windows, each one behaving like a separate terminal, as far as the programs in it are concerned. So you can run, say, your email client in one window and your text editor in another and be able to flip between them at will. The advantages to this are primarly in cases where you only have one terminal available to you.
screen supports multiple attaching. You can attach to the same screen session from different terminals. This has a couple of uses. You can have multiple xterms viewing different windows of the same screen session, giving you all the benefits of screen combined with the benefits of multiple xterms. You can also leave yourself attached on one computer (your home computer, say) and attach again from a remote computer. This is often more convenient than detaching every time.
screen keeps scrollback buffers for all of its windows. Each window has a separate buffer, and screen can use them to cut and paste between windows.
screen is friendly with various charsets, including UTF-8. It has support for entering digraphs to add accented characters and so on to any program.
screen can lock its sessions when you're not using them, to prevent others from prying into your stuff. It can run programs or lock the screen after a period of inactivity (essentially a screensaver).
screen has (optional) multiuser support. You can have different people on the same computer all attached to the same screen session and watching each other's work.
screen can split its display to show multiple windows at once, giving you multiple programs on the same terminal window.