IANAL but my understanding is that 1) it keeps your activities private when doing business as the LLC since no one has to disclose the owner of the LLC and 2) tax liabilities are not passed to the owner of the LLC, so if a business deal goes underwater the creditors can't pursue you personally.
I'm sure some details there aren't 100%. most people I know using them are privacy freaks so my experience is biased towards that end of it.