Bleed is an effect of a Skill. Most Attacks can be categorized into two distinct groups: immediate damage (standard), and Bleed damage. By default, Attacks are assumed to do immediate damage and strike foes all at once. However, many Attacks have Bleed, which means that they only do a small amount of damage but over the course of several consecutive seconds. So, for example, if a Bleed Attack in a table says 50, it most likely will do 250 damage to a monster over the course of five seconds.
Heal Bleed is quite similar to Bleed (and I don't feel it's necessary to create another whole article for it). So far, only the Majin Skill Battle Heal has Bleed Heal, which means that HP is recovered over a period of a few seconds rather than all at once. The Bleed principle is the same, but only for three seconds instead of five.