A discrete event simulation is a computer model that mimics the operation of a real or proposed system, such as the day-to-day operation of a bank, the running of an assembly line in a factory, or the staff assignment of a hospital or call center.
Simulation is time based, and takes into account all the resources and constraints involved, as well as the way these things interact with each other as time passes.
It doesn't always take exactly 5 minutes for a customer to be served and a customer doesn't always arrive every 15 minutes. Simulation builds in the randomness you would see in real life. So when you make changes to the simulation you see exactly how the system would behave in real life.
With simulation software you can quickly try out your ideas at a fraction of the cost of trying them in the real organization. And, because you can try ideas quickly, you can have many more ideas, and gain many insights, into how to run your organization more effectively.
There are many scenarios that can be simulated. As a general rule systems that involve a process flow with events can be simulated. So any process you can draw a flowchart of, you can simulate.
The processes you'll gain most benefit from simulating are those that involve change over time and randomness. For example a gas station. Nobody can guess at exactly which time the next car will arrive at the station, whether they'll decide to purchase gas only etc. Modeling complex dynamic systems like this effectively in any other way isn't possible.
There are many process improvements you can make using simulation software. For example, higher quality and efficiency from capital assets, better management of inventory, higher return on assets. But some of these improvements could be made without simulation.
So the real question is 'Why use simulation instead of another method?'