I think it's an ad-hoc term. But basically, MC simulations are needed because circuit elements such as transistors, resistors may be mismatched, for example Vth in MOS transistors. This can create input offsets in op-amps, or timing differences in logic. You can run exactly the same simulations as normally (DC operating point, AC transfer function, time-domain with many thousands of points) just over and over with new random parameters according to the distribution estimated in device characterization (I think mostly Gaussian).
Transistors models like BSIM are crazy complicated these days and there's no way to find an analytical solution for all that.
