"Есть" can be used when you ask if something exists (or state that something exists).
- У тебя есть машина? = Do you have a car?
- Да(, у меня есть машина) = Yes(, I have a car.)

If the existence of something is obvious or well-known, and it's a specific trait of this object that is discussed, "есть" usually is omitted.
У него зеленые глаза = He has green eyes/His eyes are green ("У него есть зеленые глаза" would sound extremely awkward). "У тебя есть ... глаза?" also does not sound quite right. It's as if someone has a spare set of eyes and is questioned about it.
Great explanation.