Pretty much the title.
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It depends how mathematically precise you want to be. There is a weak version, and a strong version. The ELI5 version probably isn’t precise enough to make a distinction between these.
The ELI5 version is that the average (mean) of many samples of the same random process will tend towards the true average (mean), as you take more samples.
To be more precise, for the weak law of large numbers, if we have a sequence of i.i.d.r.vs (independent and identically distributed random variables) X_i, each of which have expectation E(X)=mu, then the mean of the first n variables X_i, which is typically denoted by a bar over X_n, is a random variable which converges in probability to the expected value. By definition, this means that for any given distance epsilon from the true mean, the probability that the mean of the first n random variables is within this range of the true mean tends to 1 as n tends to infinity. So in other words, you can pick any small (but nonzero) range around the true mean, and any probability close to (but not equal to) 1, and I will be able to find a number N such that N or more copies of the random variable will have a mean within this range of the true mean with probability greater than your given value. In other other words, with enough samples, the sample mean will be arbitrarily close to the true mean with arbitrarily high probability.
The strong law of large numbers is more difficult to express in words, while conveying it’s true meaning. It basically says that if you took a sample mean for every sample size n as n tends to infinity, then this sequence of sample means will almost surely converge to the true mean: there is 0 probability that it will do anything else (converge to a different value, or diverge). I don’t know what the ELI5 version of this is. Imagine taking a sample of size 1, then a sample of 2, then 3, etc. Then you’ll get a “better” average each time. The law states that your sequence of averages will converge to the true mean 100% of the time (so if you did this many times, the proportion that did anything else would have “measure” 0; almost all of your sequences would converge to the true mean).
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