A glitch area is a glitch that involves entering a zone that is normally off limits or supposed to be non-existent. Usually, the area in question is an unprogrammed area outside of the main map that the player managed to access. This can range from a small nook to a level sized terrain. It is also common for there to be abysses in the glitch area, or sometimes the entire area is an abyss. In the end, the way a glitch area works really depends on the programming of the game it comes from.
One example is the "out of bounds area" in most pokemon games.
In most cases, the glitch area looks like a solid color, but various features from the programmed map are visible. Usually, the solid color will be whatever the skybox was in the normal area. In some cases, you will die immediatly upon entering the area. However, usually, you can explore the glitch area. However, many of these will cause the character to simply die a few seconds into it (if you did not die immediantly), and in some cases it is possible to crash the game by doing certian actions in the glitch level. While it may be exciting, also keep in mind that in many cases, there is no way to leave the glitch area.