Laws of large numbers, or LLNs, concern the convergence (in probability or almost surely) of some statistic of a random process. They say that the statistic stabilizes as the sample size grows.
The most famous LLNs concern the sample mean of iid scalar samples with finite variance. The weak LLN says that the sample mean converges to the true mean in probability; the strong says it converges to the true mean almost surely.
But one can also study LLNs in other settings, eg for medians, or for martingale difference sequences, or in Banach spaces. There is also a game-theoretic LLN. This is, in some sense, stronger than the measure-theoretic strong LLN.
You might consider ergodic theorems as generalizing LLNs.