The concept for a space elevator was actually first published in 1895 by Konstantin Tsiolkovsky but limited by contemporary materials it has until recently been a science fiction dream. These elevators is also referred to as , space bridges, space lifts, space ladders, sky-hooks and orbital elevators. Recent concepts for a space elevator propose the use carbon nano-tube, boron nitrite nano-tube or graphene based materials as the tensile element in the tether design.
The advantages of space elevators are many compared to the current way of escaping earth gravity, which is costly, risky and inefficient.
The space elevator system instead is a potentially much cheaper way of transportation. They can also provide much larger capacity than conventional rocket, allowing for access to space on a mass scale. They are more environmental friendly compared to conventional, chemical rocket engines. Once built, a space elevator would lift freight for years, rockets are one-use only. Even Shuttles were/are only partially reusable (damage taken due to heat etc.). Lastly they are much more comfortable than rockets, since they could be adjusted to be near 1 G, instead of several G-forces with rockets.
In the below TED-talk, Markus Landgraf who is a mission analyst at the European Space Agency ESA in Darmstadt/Germany, explains how to get to space via a space elevator.