The LHA's and the LHD's form the center of an Amphibious Ready Group, similar to the way an aircraft carrier forms the the center of a Carrier Battle Group. Generally speaking you have one of each type groups floating around close to each other in various places around the world. This provides a bunch of Marines and a bunch of planes to get whatever needs to be done, done.
The LHA's (like the one you saw) are about the size of a WWII Essex class carrier (the later fast attack carriers of the war). They're about the max for size that can go through the Panama Canal. They carry up to 26 CH-46s, or different numbers of combinations of aircraft, like CH-53, Harriers, etc.
There is a larger class called LHD's (Wasp class) that was designed from the begining as a multi-purpose ship. They have the same features as the LHA, but are larger and can carry about twice the aircraft and were desgined with operating the Harrier (20 of them) as a secondary mission.
Both have well decks that can flood to launch landing craft, hovercraft, etc. and both have full hospital facilities and carry Marines and their equipment including tanks, guns, trucks, LAVs, etc.
To give you an exapmle of the difference between the USN and the rest of the world, the aircraft carriers the Brits fought the Falklands war with are about half the size, and capability of an LHD. A ship we don't even consider an aircraft carrier.
Ross