It is what makes a small edge repeated many times a business rather than a gamble - the basis of both insurance and market making.
The trap. It says the average converges. It does not say deviations get corrected. In a fair coin sequence the absolute difference between heads and tails typically grows like sqrt(n) even as the proportion approaches one half. Believing otherwise is the gambler's fallacy.
Weak versus strong is occasionally asked: weak gives convergence in probability, strong gives almost-sure convergence. The distinction rarely matters in an interview beyond knowing it exists.