Why would an airport use crossing runways for takeoff and landings?
Any time the winds and traffic permit an airport may chose to use intersecting runways. You can read some interesting info on it here and here. In some cases when both runways are in use they may have the aircraft execute Land And Hold Short procedures. The pilot has the final say in a LAHSO situation and you can call no joy if you think you cant complete the maneuver as requested.

Some airports may only have 2 runways set up in an intersecting layout and may not have the luxury of parallel runways. Depending on terminal layout at commercial airports using both runways may aid in traffic flow on the ground as well as getting planes in the air.    

Winds permitting generally have to do with the maximum cross wind component of a given airplane. Although generally speaking you will see this done in calm wind situations. The other cause I have seen for this is instrumentation, some airports may have intersecting runways that are not equipped the same or of the same length. As lets say the favorable runway is is 5000ft visual approach only strip and you need 6000ft to land. Luckily the airport has another intersecting runway that is a 7000ft strip (and has an ILS approach not that you need it (its nice out)). They may have you come into the other runway while they sequence small visual traffic on to the short strip (possibly having them land short if need be).