They really do not help or correct anything. The belief that they give the horse something to lean on is misplaced, since horses balance fine with their necks. Restricting the movement of their neck restricts their balance.
They do help with one thing: if you have a rear-prone horse, putting a tiedown on him makes it much more likely that he'll overbalance and flip over.
It is used for stability for the horse.
I believe they are mainly used in western speed events (barrel racing) for the horse to brace against. It should be just tight enough for the horse to lean against with an outreached head. Other people incorrectly use them to force a horse's head down. That problem can only be fixed by correct training, not a leather strap to hold his head down.
most people use a tie down in correctly, ex. to tight. it helps with keeping your horse balanced or something to lean on while going fast speeds or changing directions like in barrel racing.