Some Pokémon have type advantage over others, so it's better to use a Pokémon with a fire-type move against an ice-type Pokémon, or an electric-type Pokémon against a rock-type one. In this battle, I quickly learned that Pinsir's normal-type Vice Grip attack was weak against Dragonite's Dragon type.
And sometimes switching Pokémon is useful because you just need to bring out one that can pack a strong wallop to take your opponent down.
So if you're battling, try changing your Pokémon in the middle of a battle and see if you can work it into your strategy. All you need to do is swipe up.