The perfect line is the best (fastest) way to make your way around a corner in (or on) a motor vehicle. In perfect conditions, the perfect line begins at the outside of a corner, comes to the inside of the corner at its apex and eases back to the outside.
In reality, the perfect line is an impossible goal, one which varies according to road surface conditions, traffic and visibility. Nonetheless, on any given weekend, wannabe racers can be found on back roads searching fruitlessly for this, the holy grail of motorsports.
But their search is not in vain, for the search is it's own reward as any motorcyclist will tell you.