The project manager usually works with other departments or teams to put the document together. They will probably use Brainstorming and Interviewing techniques to help with this process and may even build a prototype.
The business requirements document should accurately, and in detail, describe the purpose of the project. It states what is needed to achieve that goal i.e. what is in-scope, what is out-of-scope, any assumptions that have been made, any constraints that have been imposed and expected timescales.