correct me if im wrong, but i believe battle healing is the rate at which your HP replinishes automatically. the higher the skill, the faster your hp is restored during a battle. 

remember when Kirito was being attacked but basically took no damage? his healing was not only very high, but fast. If i had to guess, about 10 percent of ones HP replinishes after a certain amount of time ranging from, depending on lvl, 10 minutes to 10 seconds. that is just an example of course.

om sure if you googled it, you might find out more.