Why is good to use bootstrapping samples?

Question

I was researching a little about one algorithm called Random Forest, since it use bootstrapping samples, I mean it constructs several samples with replacement from a set, one question came to me, Why is good to use bootstrapping samples? I mean I know that the intuitive explanation is for me that if you don’t have enough data to use in order to get representative samples you need to use sampling with replacement besides if you increase the size of the bootstrap sample this sample is going to look as your original population, however in order to go more formal I would like to know if there is some result or theorem to prove it, and also if that would be possible any intuitive explanation of this result.