A flatscreen is a television or a computer screen that is very thin, more like a board on the wall than a deep box. Older screens had a heavy glass tube inside and stuck out a long way; a flatscreen sits close to the wall and does not. You can use it before a noun (a flatscreen TV, a flatscreen monitor) or as a name for the thing itself (We bought a flatscreen). People also write flat screen and flat-screen; all three are fine. The word became common when these thin screens were still new, so it can still sound a little like “the modern kind” — though actually almost every screen is flat now, so in daily talk people often just say TV or monitor and drop flatscreen altogether.