A scenario is essential a representation of a particular path through a business process.
Business processes usually have number paths that can be taken during a transaction. A simple example is when purchasing some goods, where one scenario maybe that the customer successfully completes their purchase, after receiving an appropriate credit rating. Another scenario may be that the customer has a bad credit rating and therefore the business transaction must reject the customer's purchase request.
In most business transactions there will be many different variations that could occur, and by defining these scenarios it is possible for business stakeholders to clearly define their needs (i.e. requirements), and for those scenarios to be used in subsequent phases of the software development lifecycle to ensure the system being built meets those needs.
An example of a scenario representing a successful purchase is: