A business case is a tool that supports planning and decision-making for both operational and investment decisions. A good business case includes the methods and rationale that were used to quantify benefits and costs. It shows expected profit impact and/or cash flow consequences over a period of time.
One of the big problems with business cases is that they are written by the same people who want to be funded for a particular project. These people have a vested interest and typically find a way to make their case with numbers. It gets worse when organizations rely on vendors to help them with their business case. The vendors may have some slick material and may be able to offer a few ideas for people who don't have a clue, but caveat emptor.