Brief definition - it’s a program that allows you to build your circuit, project, etc. and exercise it in a software environment.
For example: LTSpice is a circuit simulator. You can enter a circuit for a audio filter and then exercise the circuit by programming different signal inputs and watching how the circuit responds.
It’s a design tool and like any other tool you have to know how to use it, what it’s limitations are, etc. It’s not a substitute for not knowing what you’re doing - on the other hand it can be an extremely powerful learning tool. As Walter pointed out in the LTSpice class - enter the circuit and run the simulations, now go build the circuit and measure how it behaves and see how close the program was.