Schemes vary. Some give you compound interest on the amount you invest that is then just used to offset chunks of the fees at the same rate as everyone else is paying. Paying into these very early (before starting the school) gives best results.
Others allow you to use the money to pay fees at the rate they were when you put the money in, avoiding fee increases, which is very helpful in times of large increases. These often limit how far ahead the fee increase can be avoided for, or add on a certain base percentage increase after a point.
I used a scheme and stayed 2 years ahead of fees theoughout the time at a school, which meant I effectively paid the fees of between 1 and 2 years previously. I think I calculated that it saved me about £1.5k per year - it wasn't huge, when you worked out what you could earn on that amount by putting it elsewhere, but in a time of low interest rates when fees wee still rising quite a lot faster, I decided it had been worth it, but didn't save big bucks.
The other advantage is security in knowing you've paid. It's surprising how many people really scratch around and struggle to find the fees each term. If you've paid in advance there's none of this.
Re security or leaving the school, you need to ask about this. A tiny school with dwindling numbers who suddenly offering a scheme to boost its immediate income is not one to do this with. I was told and it was clear in the terms, that if we left the school early or when there was still money in our pot, we would get all of it back, as lomg as we gave proper notice. If we didn't give the term of notice, they would extract a term of fees from the advance fees pot. All of this seemed reasonable.