A spacesuit is actually a small single-occupant craft, a pressurized environment capable of keeping the astronaut alive. That is why it is so bulky and stiff: it has to maintain constant pressure inside.
The function of the team's large backpack is to house a life support system that regulates oxygen levels and removes the carbon dioxide that is generated when breathing. Known as the primary life support subsystem, this backpack contains the oxygen that astronauts breathe outside the spacecraft, and it also supplies electricity to the suit.
A fan keeps the oxygen circulating, and there is a tank that contains the cooled water that circulates through the suit that the astronauts wear attached to their bodies, and that maintains body temperature in the cold environment of space.
The backpack can be supplemented with a device called Simplified Assistance Extravehicular Rescue (SAFER). This system has several small thrusters located in different areas. If an astronaut gets separated from the International Space Station or his vehicle, he can use the SAFER to return.
Photo (NASA): Astronaut Steven L. Smith works on a 1999 Hubble Space Telescope maintenance mission. His backpack contained oxygen, a fan to circulate it, and water to regulate his body temperature.
