The document justifying an investment, evaluating the benefit, cost and risk of alternative options and giving a rationale for the preferred one.
A business case takes an established need and decides whether closing it is worth the money. It sets out the options considered, including the do nothing option that acts as the reference point, and gives the reasoning behind the one recommended. The sponsor owns it, which is what makes it an investment decision rather than a piece of analysis. It is normally revisited at each governance gate, because estimates mature and options fall away as the work proceeds, and the justification is re-tested against the better information.
See also
Structured work establishing the gap between an organisation's current state and the state it requires, in evidence, before any solution is named.
The written output of a needs assessment: the gap an organisation has to close, described with no product, technology or supplier named in it.