Derailleur hanger is a metal extension of the rear dropout through which a rear derailleur is mounted. If the rear derailleur is damaged, mostly likely the derailleur hanger could be damaged as well and has to be replaced. It's also recommended to carry a spare derailleur hanger when riding a mountain bike.
Below is a reference of compatibility list. On top of that, please always compare the geometry of your original derailleur hanger with that in the picture to make sure you are purchasing the right part.

Cannondale Bikes: Bad Boy : 2011
Cannondale Bikes: Bad Boy: 2011
Cannondale Bikes: Trail SL 29er: 2011
Cannondale Bikes: Trail SL: 2011
Cannondale Bikes: Flash Alloy 29er: 2010
Cannondale Bikes: Flash Alloy: 2010
Cannondale Bikes: Lexi : 2011
Cannondale Bikes: Lexi: 2011
Cannondale Bikes: Quick CX 1-4: 2011
Cannondale Bikes: RZ 120: 2011
Cannondale Bikes: Scalpel 3rd gen: 2010