Many games allow the player to control the camera, typically through the use of an analog stick in the case of a controller, or by movement of a computer mouse. Taking a console first person shooter as an example, by default moving the stick upwards will pan the view upwards, and moving the stick down will pan the view downwards. For some people this isn't intuitive however, as they link the movement of the stick with the back of the head of the character they're playing . As a result moving the stick forward would make the head tilt downwards, which should make the view pan downwards with it, and vice versa for pulling the stick backwards. In other words (particularly in third person games) when the controls are inverted, what you are really doing is rotating the camera up and over the characters head so it is then looking down.
Another inversion of camera controls is found in third person games, where some people prefer to have the sideways movement of the camera around their character inverted, so that moving the stick left would make the camera pan right etc.
These options are offered primarily to increase the usability of a game and allow great amounts of people to play without the game feeling weird. In the same way that some games offer the ability to swap the left and right analogue sticks it's about catering to a wider audience.
The inversion of camera controls is a controversial subject in some gaming groups, since playing with controls that are the opposite of what the user finds intuitive very quickly becomes a huge annoyance. Because the majority of players prefer un-inverted controls, sharing a controller between a group of people where one individual uses inverted controls can be a hassle, depending on how cumbersome the game's control options screen is. This results in a slight ghettoisation of players that prefer inverted controls. However there is almost a universal agreement on inversion of controls in games that feature flying vehicles, such as helicopters and planes, because in such situations the analog stick will simulate a flight stick.