I think some web history is kept on your google account. So if your home computer is signed into the same google account as on your phone you will see history from there as well.
But in the browser----Menu Button-----More----Settings----Scroll down to clear history.
Did some searching and some people are saying that it doesn't work.
Tried it on both my android phones (Galaxy I, Droid Charge) and it worked fine for me. Both phones running Android 2.2.
I don't know anyone with a Samsung Ace, sorry.
