SAP = Systeme, Anwendungen, Produkte (Systems, Applications, Products)
But they don't really use that name any more.
It is an Enterprise Resource Planning system. Basically a collection of a whole lot of different applications to help run a huge corporation's business. You can pick and choose which modules you want to implement. It can do everything from managing inventory to shipping to production planning to handling all the HR stuff (payroll, etc.).
EDIT: I should correct myself and say that SAP is the company name, but when someone in IT says SAP, they are usually talking about the application itself.