The win streak offers bird boosters for completing levels in a row without failing any levels. The longer the win streak, the more birds you can have.
Beat a level to complete the first stage of the win streak, and start the next level with 1 free Red birds booster. Pass the next level, and you'll begin to the following level with two boosters, 1 Red and 1 Chuck. Finally, beat the third level to complete the last stage of the win streak and start the next level with three boosters, 1 Red, 1 Chuck, and 1 bomb. If you continue your win streak beyond three levels, you'll continue to start each level with three bird boosters. However, if you fail a level at any point, you will lose the win streak and have to start over from the beginning!