In the manual, it's called drifting and power-sliding. The boost you get after the sparks under your wheels turn blue can happen anywhere, not just behind an opponent. If you're turning, press and hold R as you will see your character bounce into a drift. After that, immediately press right on the control pad then then back to holding left. You will began to notice red-orange sparks coming out of your tires. Repeat that once again and they will turn blue. When you release R, you will get a mini-boost.
If you're talking about that strange wind-like thing that comes about some times when you're behind the racers, I don't know. As far as I know, it comes about randomly when you're in at the most, fourth place. Some times it lasts for a while... I'm sure Aarom11 will know. He's the expert. XD