If I owe you money, then I need to remunerate you. To remunerate is to pay money that is owed.
It's nice to be remunerated — that means someone paid you money that was owed. If an employer makes you work overtime, they will need to remunerate you for that. If you lost your dog, offered a reward, and then someone found the dog, that person should be remunerated. When you see remunerate, think "giving someone money they deserve."