The official reason is this people in Libya, inspired by an uprising in Tunisia, rose up in an attempt to overthrow Gadaffi. Gadaffi his hit back violently and is using every means at his disposal to kill and smash the rebellion.
Dave has insisted that there should be a no fly zone thus preventing Gaddffi's air force from bombing civilians. However there are already reports that allied air action has caused the death of civillians. This of course will be called "collateral damage", you can't make an omellette without breaking eggs etc.
In the meantime in Bahrain and Saudi arabia there are revolts which have been equally brutaly put down. However reporting is sketchy at best and the are no allied actions over this.
Also as I said Dave justifys this by saying we have to get rid of a despot, meanwhile in Zimbabwe Robert Mugabee kills people willy nilly and Dave stays shtum.