Jesse explained the meaning well. The problem here is the example sentences - sentence 1 is perfectly OK, it is grammatical and clear. Sentence 2 is using 'as to' as some kind of ketchup to make the language more tasty, but in fact it spoils the dish. If you try substituting Jesse's alternatives (e.g. 'concerning' for 'as to') in sentence 2, you can see clearly that they don't make sense; 'as to' makes no sense here either. Adding it does not make the text more formal, it simply seems to, unless you look closely. This is a technique used by poor writers to disguise their writing and make it seem impressive, but it only works with poor readers. As to the correct usage of 'as to', it is a way of changing the subject of discussion by introducing a new topic (or reintroducing an old one), as I just did here.

Hi :D "as to" is used to mean "with respect to or concerning" so if we say I don't know as to why she went there to meet him, you are just stating that you don't really know the reason behind her going to meet him. I would say, the only difference is the way it is being phrased, "I don't know why" is definitely easier to say compared to "I don't know as to why" Other than that, they convey the same meaning pretty much except one is a bit more formal and the other one is more casual.