I've mentioned use cases on a number of occasions, but equally important is the concept of scenarios.
A use case is a sequence of interactions that the user makes with the product to achieve a goal. Think of a use case as encompassing any number of scenarios. A scenario is specific instance of a use case with a very specific goal.
For example, if your product is a car, one use case for the product would probably be Drive Car. The Drive Car use case encompasses infinitely many specific scenarios, including one in which a customer drives the car from her home to the Walmart on the other side of town. All of the specific circumstances are part of the scenario, including how fast she drives, how many stop lights she encounters, etc.
Thinking about (and actually testing) scenarios gives your team a concrete and tangible idea of what your customers will experience when they use your product. It also forces your team, particularly the product manager, to consider what scenarios they should realistically expect customers to carry out.
In short, if your team fails to consider and test scenarios, they will tend to become disconnected from the real customer experience, leading to a product that is similarly disconnected. A skilled product manager who stays connected to the market can help avoid this problem.