A bandage is an item that can be applied to the using character or a friendly target (player character or their pet) that restores health over a period of time depending on the type of bandage.
Bandaging has a cooldown timer of 60 seconds after you use it before you can use it again.
Bandaging is a channeled effect. Taking damage while bandaging, be it from a direct attack or a DoT, will interrupt the application, ending the process and so severely reducing the amount healed. However, unlike other channeled effects, damage absorbed by a shield effectwill cancel bandaging.
These tips are mostly for classes without any other healing ability.
It's a close fight. Health is low and healing potions are not an option. You need healing or you're going to die. Your escape path is blocked. What do you do? stun/root/sheep or otherwise render your enemy unable to attack you and then bandage.
Beware, DoTs will interrupt a bandaging attempt, so don't use while under a DoT because it will still start the cooldown timer for bandaging and prevent you from using it if you need it soon after.
Although wasteful, with good timing (and practice) you can bandage even while being attacked. The few thousand precious hps from a tick or two can turn the tide of a very close battle.
Several types of bandage can be sold to vendors for more than the cloth used to make them, so rather than vendor the cloth, make bandages and sell them instead. However, selling the cloth on the Auction House is often far more lucrative than selling to vendors.