がほしい means "to want" in the sense of desiring to have something. The thing wanted is marked by が. It is an adjective (い-adjective) and conjugates like one: ほしい, ほしくない, ほしかった. You use it when you want an object or a person's presence, but not for actions. For actions, you use たい form (e.g., 食べたい).

This pattern is common in everyday conversation. In polite speech, you add です: ほしいです. In casual speech, you can just say ほしい. It is fine to use with friends, family, and in most informal situations. However, be careful: saying ほしい about someone else's desire is not direct; you need to use expressions like ほしがる or ほしいと思っている. For your own wants, it's fine.

When you want something that is not a physical object, like a pet, a car, or a person's help, the same structure works. For example, ねこがほしい means "I want a cat." Also, が is often replaced by は in negative sentences for contrast, but がほしい is the base.