The official missions of each branch give a pretty good example of what each branch's mission is:
Note: sustained land dominance. The Army's job is to take and hold land, and is thus geared for land combat on a large scale and for long duration missions.
The Navy is, not surprisingly, oriented towards naval combat in all aspects - from naval aviation to submarine warfare to special operations conducted on water.
The Air Force, also unsurprisingly, is focused on fighting in the air through gaining air superiority, which can only come with well trained pilots and well maintained aircraft. Also, the Air Force is focused on space and cyberspace, and has a lot of technical work in that area.
The Marines are designed as naval infantry, and are thus oriented around combat on land from the sea. They work closely in conjunction with the Navy, who provides the ships capable of moving the Marine around the world. They're also designed as expeditionary forces, ready to deploy at a moment's notice (faster than the Army by design) with all the supplies and equipment needed to sustain themselves for a period of time.