Clarified that drivechip refers to a DVD modchip, as there are others like Infectus that are unrelated.
Drivechips (a.k.a. modchips) are used to inject code into the Panasonic MN10200-based microcontroller in the disc drive. The firmware on this chip is stored in mask ROM, but is loaded into RAM before execution; these chips use debug commands to patch the firmware in RAM upon boot, generally to defeat the protection against recordable DVD media.
These chips are most commonly used for run copies of original games (most of the time illegal ones), but they did also play an important role in the early stages of Wii homebrew development. A drivechip can be used to run GameCube homebrew on the Wii, and if you haven't updated to system menu 3.3, [[Signing bug|fakesigned]] Wii homebrew.