When you turn the tide, you change things — usually dramatically, and for the better. When a losing candidate starts winning, her campaign manages to turn the tide.
If you change the course of a bad situation, you turn the tide — like when your hard work training your puppy results in a calm, clean house instead of your previous life of chewed up shoes and constant barking. When you reverse someone's opinion, you also turn the tide. This common phrase reflects the change that occurs when a rising ocean tide starts to recede, or go out.