Cheating in video games usually means two different things, but they have in common that they change the game for the user, usually making the game easier in some way.
This is the somewhat accepted form, and usually involves entering a code that the developer put in the game to gain an advantage such as;
Unlimited lives/ammo/other advantages specific to the game such as sprinting
Random fun stuff (For example a gravity cheat in Grand theft auto)
These kind of cheat codes are only seen for single-player games (for obvious reasons) and are generally used to help players either overcome a difficult encounter or let them have more fun. However some people believe that you rob yourself of the experience of both playing a game the way it was intended and feeling successful when completing something hard.
A popular type of cheat code is the Konami code.
Cheating through external programs
Preventing cheats (usually known as implementing a form of anti-cheat) is of major focus to every developer who is developing a multiplayer game today. This kind of cheating usually involves some form of external program running at the same time as the game.
This is also the reason why cheating in multiplayer games is a much more common phenomenon on the PC since it is much easier to run programs and files on a PC, whereas doing this on consoles is a complicated thing that usually involves opening and modding it or buying an external device designed for cheating.
This kind of cheating is of major annoyance to the other players who are the victims of the cheater, and if detected will often result in a ban of either account or CD-key.
The kind of advantage given by this kind of cheating depends on the type of game.
In a First-person shooter cheaters might have the ability to see enemies through walls, or have their weapon automatically aimed at opponents.
In Real-time strategy games cheaters might have the ability to see the entire map (beyond the fog of war)
This kind of cheating is usually a breach of the agreement that players accept when they install a game, since it involves external programs modifying game files, and it effectively ruins the fun of other people which is why most game companies go to great lengths to ensure that this form of cheating is either hard, impossible or can be detected and punished. This usually results in an ongoing battle between cheaters and developers where the cheaters try to remain undetected and the developers keep patching their anti-cheat program so it can detect the newest cheats.
Because of the major griefing involved with this kind of online cheating, players who do it are usually looked down upon by the rest of the community.