What is a "barrier option" and hoe does the Greeks look like?

An option with a strike price and a barrier price. This barrier price make the option cheaper than a regular option. 

 

Knock-in barrier options: if barrier breached, options come into existence

--- down and in

---up and in

Knock-out barrier options: if barrier breached, options cease to exist

--- down and out

--- up and out

 

Opposed to regular options; here a vega can be negative. Too much volatility increases the possibility that the barrier is hit.

More difficult to hedge, because the delta is discontinuous at the barrier.