Official Wii game discs are pressed, and in such a way to contain information that you can't put on a disc by burning it. an IOS can call two different functions (simply put) to the disc drive, one of them is the wii-disc read command; the disc drive does a build-in (in the firmware of the disc drive = untouchable by wii software) check to see if the pressed 'secret' info is present on the disc (so it knows the disc is official) and then reads the data at 6x speed.
The other command an IOS can send to the disc drive is a dvd read command. The command is recognized by the disc drive, so nintendo had the plan to make the wii read dvd's out-of-the-box, but they dropped it. Otherwise, the command wouldn't even be recognized by the disc drives firmware (it had to be build in). When the disc drive gets the dvd read command, it doesn't perform the check for 'pressed information', it just reads the data, but at 3x speed (dictated by the drives firmware).
A modchip basically takes over the job of the disc drives firmware (I'm not very familiar with this, so I could be wrong on the specifics), and makes sure that even when the wii sends a wii-disc read command, the 'pressed information' is NOT read and the data is read at 6x speed, thus allowing burned discs to be read at full speed.