This isn't exactly the most unknown principle out there, and chances are you know what this means already, but just to make things crystal clear: the law of large numbers means, at least in the context of this article, that if you repeat an experiment enough times, you're bound to get every possible outcome at least at some point. Fore example, if you're a traveling salesman, you're more likely to get a sale if you knock on every door in an apartment building than if you knocked on the door of one single detached house. Makes sense, right?
But naturally, I'm not talking about salesmen specifically here - although if you are a salesman by profession, this example perfectly captures the effect of the law of large numbers to you. Nevertheless, this law applies to basically anything. If you're an aspiring entrepreneur, you're more likely to succeed if you try out different business ideas 300 times than if you try out just one or two ideas and then call it quits. If you're a brain surgeon, the chances of a succesful surgery increases with every surgery you perform, and naturally a surgeon with a record of a hundred operations is a better surgeon than a surgeon who's just getting started.
It's kind of like practice makes perfect, although not quite.
The law of large numbers also means that if you roll the dice a thousand times, each number from 1 to 6 will appear approximately the same number of times. It also means that if the universe is cyclic and everything goes from the big bang to evolution to reducing back to a singularity that produces another big bang, and this goes on until eternity, literally every possible event will happen eventually. Neither of these will exactly help you - but the idea of trying until you succeed does.
Whatever you're trying to achieve with your life, remember this: virtually no one gets it right the first time. Some people have tried hundreds of times before succeeding. You're most likely somewhere between those two.