Looks like a Ender Dragon....but smaller. It is not hostile nor is it large enough to fly.
You tame it by feeding it warp bones. Once you do that it will stare at you, blankly. If you then feed it a ender flesh then it will have blue eyes instead of purple (or red if you atack it). Once that happens you give your dragon a name. This is so on a multi-player server other players dont mix them up.
The baby ender dragon is fed warp dragon meat from end traders or a recipie. Then feed it to your dragon and it will be happy entering love mode (only mates in tier 6 romp higher.) once you feed it 5 times it goes into the next teir:
Tier 1: Follows you...ummm doesn't do much.
Tier 2: kills enemies, similarly to a Wolf. Had 30 HP and does 5 damage.
Tier 3: more damage (10)
Tier 4: MOAR damage (15)
Tier 5: purple fire balls! (One per 3 seconds and deals 20 damage)
Teir 6: can mate
teir 7: can fly!
Tier 8: MOAR DAMAGE!!! (25)
teir 9: more purple fire balls (3)
teir 10: MORE DAMAGE FIREBALLS AND CAN CARRY YOU!!! (35, and 5)
what they do
they act like wolves. Except lead by a ender nest keeper.