That's a saying that circulates in Britain, and I've heard variants in the US too (usually the number of falls).
I'm well past my ten falls, as it were (I'll be honest and say I'm thinking of this topic because I took a stupid tumble yesterday, off of the tallest horse in the barn, because I do nothing by half measures) - but what the saying really means is this:
If you worry too much about falling off, you will never progress as a rider. An occasional failure to keep the horse between you and the ground is a normal hazard of riding - and something you have to learn to deal with.
It might not take ten falls to be a good rider, but you can't become a good rider without falling off.