It works because artificial neural nets take a lot of examples of something to learn it (way more than natural neural nets). So at the simplest level it's just copying items in the training data enough that they become salient.

More complex synthetic data generates things that could be in the training data but aren't for some reason. For example, machine translation training corpuses often contain a lot of formal language (because formal documents are the ones that get translated), so you might generate a bunch of casual conversation to improve the translation model's ability to handle that.