What does it mean to simulate a quantum system? What does it mean by simulating quantum system? Can I simulate Young's double slit experiment with a quantum computer? If yes, won't it violate no-cloning theorem?
 A: To simulate means to mimic or model the characteristics or appearance of something. Cloning means to make an exact replica- another actual instance of the subject being cloned. The two actions are utterly different in essence. So yes, you could straightforwardly simulate the two slits experiment, and no that would not violate the no-cloning theorem.
A: There are two aspects to this question, I'll start with the second one:
No-Cloning theorem:
It's important to understand the actual statement of this theorem:

There is no unitary operator $U$ on $H \otimes H$ such that for all normalised states $|\phi \rangle_A$ and $|e\rangle_B$ in $H$:
$$U(|\phi\rangle_A |e\rangle_B) = e^{i \alpha(\phi,e)} |\phi\rangle_A |\phi\rangle_B$$
for some real number $\alpha$ depending on $\phi$ and $e$.

What's important to note is that no-cloning theorem is concerned with copying unknown states. If you know what $|\phi\rangle_A$ is or you know how to prepare it then you can obviously use a unitary $U$ that is tailored towards $|\phi\rangle$ and make as many copies of it as you desire, without violating the no-cloning theorem.
Simulation of Quantum Systems:
As Marco Ocram said in his answer, simulation has to do with modelling a physical system with some computational tools in order to extract some information about that system. These simulations could either be classical or quantum. Experiments, in their pure form can be considered to be a computation. Usually one considers a universal computational model, e.g. a universal set of quantum gates, or a Turing machine. These models are universal so any computations can be carried out with them, so we can utilize them to get results without having to do the actual experiment.
