Each leg of the teaser has to hit in order for the ticket to cash. If you are looking at an 8-point favorite, a 6-point teaser would now require them to win the game by more than two points instead of eight.
If you are looking at a 3-point underdog, a 6-point teaser would now give them nine points in the game.
The most common teaser is in football where bettors get six points added or subtracted from each of their point spreads. A teaser is a special kind of parlay where the bettor gets assistance on the point spread on multiple games for a decreased payout.