Requirements gathering sets the stage for the rest of the waterfall process, and is critical for understanding the needs an scope of the program you will be developing. This process begins with obtaining business requirements from the customer, and should include input from all stakeholders. This information is gathered through formal information-gathering processes borrowed from the social sciences.
These business requirements should be broken down into functional requirements fine-grained enough to give the developers a clear picture of what the software will need to accomplish. Moreover, they need to be comprehensive enough to not leave developers with unanswered questions. For novel functional requirements prototyping and brainstorming can be useful in sussing out possible implementation approaches and their feasibility.
The outcome of this process is a comprehensive document detailing the requirements of the software. It will commonly include sketches of proposed user interfaces and a discussion of how the software will integrate with other systems. It is also common to identify priorities of the various requirements.