volitional form; let's do ~
Expresses suggestion or invitation to do something together, like 'let's do ~'.
The volitional form is used to suggest doing something with others or to express your own intention. It's the 'let's' form. For example, if you want to propose going to eat, you say 食べに行こう. This is a very common, everyday pattern used among friends, family, and colleagues. It's not rude, but it's casual and friendly. In more formal situations, you might use ましょう instead, but 意向形 is fine for most social settings. When using this form, you're including yourself in the suggestion, so it's not used for ordering someone else to do something.