If you're in Thailand on a temporary visa and move to a new address in the Kingdom, such as go to a different province to stay with a friend, or relocate, then you need to notify immigration of your change of address within 24-hours. As with all things immigration, if you don't you risk being fined.
As it was explained to us, if something goes wrong and the police need to find out where you are (to ascertain your whereabouts, your safety, that kind of thing), then they will go to that address. If, of course, you're in another province and haven't told the relevant authorities, they won't be best pleased.
So, make sure you do it.