A mouse is an input device used to move the cursor on a computer screen. Using a sensor, it detects movement in two dimensions, translating that movement to the cursor onscreen. In the past, mice came with a PS/2 connector to plug into the computer, but most mice these days connect to the computer via USB 2.0. Gaming mice are a subsection of mice that are focused on customization, sensitivity, and number of buttons.
One defining characteristic of a mouse is the type of sensor used to detect movement. These can take several forms.
A Laser mouse uses an infrared laser to illuminate the surface below the mouse, and a sensor to track changes in that surface. Some forms of laser mice are able to be used on a clear glass surface, unlike some other types of mice. This type of mouse is in wide use today.
An optical mouse operates in a similar manner as a Laser mouse, only it uses a LED to illuminate the surface below instead of a laser. Like the Laser mouse, this type of mouse is popular today.
A Mechanical mouse uses a rubber ball set on a series of tracks to detect movement. These mice are easy to open, and therefore easy to steal the ball from. They also attract dirt on the tracks easily. These mice are no longer in widespread use.
A Trackball mouse uses a plastic ball suspended inside the mouse to detect movement. Rather than moving the entire mouse around, the user rolls the stationary ball in the direction they want the cursor to go. This type of mouse has been shown to reduce wrist strain compared to other mice.
While all of the above are available in both wired and wireless forms, using wired mice is recommended as wired mice have less latency than their wireless counterpart.
Most modern operating systems (including nearly all Windows releases) have native mouse support, and drivers are not required. Some mouse drivers offer advanced features, such as button remapping or battery monitoring, but these are usually optional. It is recommended that if your mouse came with a driver, you should install it, as those additional features will likely not work without the manufacturer provided driver.
Certain high-end gaming mice allow the user to customize their mice. These mice allow the user to add or remove weight to the mouse, or adjust the position of those weights. Some mice also allow the user to change the angle or size of buttons or finger rests like the R.A.T gaming mouse from Mad Catz.
The user is also able to customise their mouse by rebinding many of the buttons. For more information on this, see Remapping.
One important consideration of any mouse is the sensitivity, measured in DPI or Dots Per Inch. This refers to how sharp a 'picture' the sensor can take of the illuminated surface below the mouse. A sharper image allows the mouse sensor to more easily detect changes in the surface, and thus detect movement. The higher the DPI, the less movement you have to make to move the cursor the same distance on the screen. Most gaming mice allow for DPI up to around 8200, at which point you can do a 360° turn in most games with very small movements. Some people however prefer to play with lower DPI (about 800-1600) as it is more deliberate and less twitch based.
Most gaming mice allow you to change the DPI lower or higher in the middle of gameplay. This can allow you to more quickly adapt to changes in gameplay. For example, in a class based game like Team Fortress 2, you may want to change the sensitivity of your mouse based on the class you pick as the situation changes. You can for example play sniper and lower your DPI when you zoom in to get headshots for better accuracy then switch it back to normal when moving around.
Most standard mice come with 2 buttons and a scroll wheel. This is the bare minimum that most games expect you to have on your mouse. However, most gaming mice will have anything in between 4 and 20 buttons, which can then be used to activate macros (when paired with the right software). Many games today will recognize these additional buttons, which can also be assigned actions just like keyboard buttons. These buttons are placed to be easily accessible, and can be reached faster or more comfortably than some keyboard buttons.
Most basic mice are ambidextrous, and can be used by either left-handed or right-handed people. Many mice, especially gaming mice, however, are designed specifically for the right hand. Left-handed mice are very rare. There are companies like SteelSeries that produce mostly ambidextrous gaming mice. Using a right-handed mouse left-handed is not recommended, as it can cause strain or damage to the hand, wrist, and arm.
Mouse article on Wikipedia
Gaming mouse resource