# meaning of 'Monte Carlo' in this sentence

This is from a paper 'Algorithms for Inverse Reinforcement Learning' by Ng, Russell (2001)

We assume that we have the ability to simulate trajectories in the MDP (from the initial state $s_0$) under the optimal policy, or under any policy of our choice. For each policy $\pi$ that we will consider (including the optimal one), we will need a way of estimating $V^{\pi}(s_0)$ for any setting of the $\alpha_i$'s. To do this, we first execute $m$ $\underline{\text{Monte Carlo}}$ trajectories under $\pi$.

Sorry for the long quote. What is the meaning of 'Monte Carlo' in the last sentence?

My first thought would be to just run the simulation again and again $m$ times. But rethinking it, I might be very wrong.

What Ng and Russell seem to be saying is that for each policy $\pi$ they simulate $m$ "possible" outcomes for processes starting at point $s_0$. By "trajectories" they seem to mean the possible developments in time of simulated processes -- different possible scenarios created by simulation. So you were correct, Monte Carlo stands here for "simulation" (see also this thread).
Monte Carlo here simply means use sampling to estimate the values. Practically this means collecting a sequence of (state, action) pairs, i.e. the trajectory using some arbitrary policy, and from this you can compute relevant quantities like V, etc