It's not clear where this phrase originates from.
It was written in the Farmington Enterprise newspaper from 1809, where a man is relating to another about his time at the circus:
"'Say,' said Tommy, 'did I ever tell you about the circus we had at our house the other night?'
'No,' said I, settling back in my chair, 'let her rip.' "
In a book titled Out West, published in 1910, the phrase is used with its 'go faster' meaning,
"Git up more steam--this ain't a funeral! Let her rip! Don't mind the speed limit! Keep the whistle going!"
So the phrase has two different meanings, one is with speed and the other is with starting something.
Well, there is another meaning which I have no idea where it came from but it has to do with a bodily function. Yeah, you know what that meaning is.
It's unfortunate that the only good graphics or memes I could find to illustrate this phrase is this one...