Refer to figure.
When the taxiway is designed, the designer assumes that planes will be manouvred in such a way that the cockpit stays above the centre line markings of the taxiway. This allows the designer to make the corners wide enough to allow for the movement of the correct sized aircrafts. Some aircraft with very long wheel bases will "cut the corners" with their outermost inside main landing gear, so the design of the taxiways must accomodate this.

This does make taxiing a large aircraft much easier for the pilots, who simply have to keep themselves sat on the centre line.