Drag Racing is one of the 4 mini games in Kart world which can be selected from the minigame menu, its on the top left. the aim of the game is to get accross the line before you opponant does by shifting the gears on ur car at esactly the right time, you click the gear stick when the lights get to the green box, change too soon and you'll loose some power, change to late and they'll be there first.
Whenever you win a drag race (with exception of the ones during the story) you will be gifted a nitro boost, more may also be bought for 1 cash. you can hold up to 3 N20 canisters as indicated on the display and activating them via the space bar can give you a much needed boost in speed that could help you overtake your opponant.
The key to winning a drag race is to accelerate quickly off the line, you will need to pick Karts with high acceleration and top speed to stay ahead, handling doesn't matter in drag racing since you are driving in a straight line. one good kart for drag racing would be the Vampyre as it focuses purely on top speed and acceleration.