This law is similar to the weak law, but deals with the convergence of the mean. Let $X_{i}$ be $n$ independent identically distributed random variables with mean $\mu$. Then the mean $M_{n}$, \begin{align} \lim_{n \to \infty} P(M_{n} = \mu) = 1 \end{align}
That is, $M_{n}$ converges to $\mu$ with probability $1$ or almost surely. Convergence with probability $1$ implies convergence in probability, but the converse is not always true.
There is a subtle differnce between WLLN and SLLN. WLLN states that the probability of deviation of $M_{n}$ from the true mean is always finite, although the probability of deviation converges to $0$ in the limit. On the other hand, SLLN states with absolute certainty that in infinite experiments, the sample mean will converge to the true mean with probability $1$.