Well the saying is a reference to the 1989 hit song of the same name by Milli Vanilli. It was a huge single and made it all the way to number one on the Billboard charts RIIIIIIIIIIGHT before Rob and Fab were outed as frauds who couldn't actually sing a lick.

That's where the reference comes from anyway.

As to what it really means? You're guess is as good as Rob and Fab's. But in context of the song, a guy lost his lover due to his foolish pride but refuses to acknowledge that its his fault. So since he has to blame it on something aside from himself, he blames it on the rain. Which makes the saying basically a nod to ridiculousness when you refuse to man up to your own inadequacies and shortcomings. Blame it on the rain has become something you say when you have to blame something.

Of course, you could also blame it on the rain if you were supposed to go out on a hot date but you flaked because of a torrential downpour. Believe it or not, torrential downpours are completely legitimate reasons to not show up for a date. Now in 1989 you couldn't text anybody that you wouldn't make it, you had to call. But today, you can just send a text saying that its raining (in case they don't know) and reschedule - all without actually exchanging a spoken word. I would advise against this however since chicks don't like the text message brushoff.

But hey, it isn't your fault anyway. It's the rain's fault.

Thank you Milli Vanilli.