GoKawiilTwo of the biggest factors to look at in a gaming mouse are input latency and polling rate, two closely related stats that determine how responsive your device will be while gaming. Latency is how long it takes between taking an action (clicking and movement) and when it appears on screen, and polling rate is how often your mouse is communicating actions to the computer. Polling rates are measured in Hz — your average office mouse may operate at 125Hz, communicating every 8 milliseconds; a high-end gaming mouse can often reach 8,000Hz, communicating every 0.125 milliseconds.
Dots per inch (DPI) and inches per second are two other features to consider, though the former is generally less important to the pros. Dots per inch is essentially how sensitive your mouse is, measuring how much the cursor will move with every real-life inch the mouse travels, while inches per second (also called tracking speed) is how quickly you can move the mouse before it's unable to accurately keep up. A high tracking speed is very important, ensuring any fast movements can be communicated with precision, but an overly-high DPI can actually be more of a hindrance, picking up even the slightest unintentional hand twitches and interference from the mousepad due to oversensitivity.
The final consideration is more down to personal preference: the actual build of the mouse. Things like weight, ergonomic mouse structure, and how many extraneous buttons it has are all factors that determine the perfect device. Those who play games with lots of hotkeys will appreciate a mouse with a selection of side buttons, while a gamer primarily focused on first-person shooters might value a feather-light mouse more for quick movements.