Monte Carlo methods are a class of algorithms that uses random samples to obtain numerical result. Some common tasks that can be solved by Monte Carlo method includes numerical integration.
In the context of algorithms, Monte Carlo algorithm is a randomized algorithm that produces approximation and relies on the law of large numbers and central limit theorem to converge to a reasonable result as the sample count increases. This contrasts with Las Vegas algorithms, which always produce deterministic results but may have none-deterministic runtime.