Most of all rockets we see have a bell-shape cone at the bottom to direct the exhaust of a rocket engine. With the proper guidance of the rigid nozzle made of a thermally stable material, the exhaust, which is a high-temperature mixture of water vapor with a small amount of chemical propellant, go in the right direction to provide thrust to the rocket, instead of dispersing randomly in all directions.
This works fine in the ambient air. But once the rocket reaches the upper atmosphere where air pressure decreases, the thrust-generating exhaust start to travel outside of the main exhaust plume and reducing the efficiency of the engine.
Decades ago, rocket engineers came up with a new type of engine with a spike-like structure at the outlet of the exhaust. The wedge-shaped protrusion forms one side of a virtual bell, with the other side formed by the outside air—hence the name "aerospike engine".
For both technical and economic reasons, aerospike engines have not made it to the mainstream of rocket industry. Among many space-traveling vehicles that were proposed to use the aerospike rocket engine, the Lockheed Martin X-33, an unmanned, sub-scale suborbital spaceplane, is probably the most famous one.
Initiated with the support of NASA around the early 1990s, the program was however canceled in 2001. The causes? The engine was reported to have made the flight unstable and added extra weight. What was more detrimental, the engine's composite liquid hydrogen fuel tank also failed during testing: tiny cracks were found on the wall of the tank.
Source: Curious Droid via Youtube