First of all, there's many, many different types of simulation in statistics, and even more in the surrounding fields. Just saying "Simulation" is about as useful as saying "Model" - that is to say, not much at all.
Based on the rest of your question, I'm going to guess you mean Monte Carlo simulation, but even that's a little vague. Basically, what happens is you repeatedly draw samples from a distribution (it need not be normal) in order to do some statistical analysis on an artificial population with known, but random, properties.
The purpose of this tends to fall into two categories:
Can My Method Handle X?: Essentially, you're simulating a series of many random populations with a known "right" answer to see if your new technique gives you back said right answer. As a basic example, lets say you've developed what you think is a new way measuring the correlation between two variables, X and Y. You'd simulate two variables where the value of Y is dependent on the value of X, along with some random noise. For example, Y = 0.25x + noise. You'd then create a population with some random values of X, some values of Y that were 0.25x + a random number, likely many many thousands of times, and then show that, on average, your new technique spits out a number that properly shows that Y = 0.25x.
What Happens If? Simulation can be done as a sensitivity analysis for an existing study. Lets say for example I've run a cohort study, but I know my exposure measurement isn't very good. It incorrectly classifies 30% of my subjects as exposed when they shouldn't be, and classifies 10% of my subjects as unexposed when they shouldn't be. The problem is, I don't have a better test, so I don't know which is which.
I'd take my population, and give each exposed subject a 30% chance of switching to unexposed, and each unexposed subject a 10% chance of switching to exposed. I'd then make thousands of new populations, randomly determining which subjects switch, and re-run my analysis. The range of those results will give me a good estimation of how much my study result might change if I could have correctly classified everyone.
There is of course, as always, greater complexity, nuance and utility to simulation, depending on how much you want to dig.