Requirements Elicitation is about discovering the real business requirements and the system requirements of any software endeavour. It is first about discovering what is needed and then about articulating the distilled discoveries into a artefacts that can be used as the basis for describing what needs to be done. It is unusual that the real business requirements (and subsequent system requirements) can be rapidly found. Although requirements elicitation is sometimes referred to as requirements gathering, this is a misleading phrase. The real requirements are more like buried treasure in a field as apposed to crops that can be reaped. Sometimes an indication of the requirements are documented, sometimes not and sometimes what the user thinks they want, is not in fact what they actually want or need.
Documenting requirements is challenging, but eliciting the right requirements can be even more so. Doing poor elicitation will lead to the wrong software being built, can be a partial or complete waste of the entire activity.
Requirements elicitation is usually performed by a trained and qualified Business Analyst. Their responsibility is not only to identify the business needs and value but also the risks, and assumptions associated with the endeavour.