A cinch is a strap that holds on a saddle. It is also a word for pulling anything else in tightly. For example, a corset cinches in your waist.
Finches are small, seed-eating songbirds. They come in a huge variety of colours and patterns, and can be found all over the world. Many finches are very pretty and make good pets.
You pinch something when you grab it tightly between your forefinger and thumb. Pinching is also a word for any similar motion to pinching with your hands, or something that feels like pinching. For example, "my new shoes pinch my feet".