A hypergolic propellant is either of the two rocket propellants used in a hypergolic rocket engine, which spontaneously ignite when they come into contact. The two propellants are usually termed the "fuel" and the "oxidizer". Although hypergolic propellants tend to be difficult to handle because of their extreme toxicity and/or corrosiveness, a hypergolic engine is easy to control and very reliable.
Soviet rocket engine researcher, Valentin Glushko experimented with hypergolic fuel as early as 1931. It was initially used for "chemical ignition" of engines, starting kerosene/nitric-acid engines with an initial charge of phosphorus dissolved in carbon disulfide. German professor Otto Lutz independently discovered the principle again in 1935. The Wac Corporal rocket developed in the USA by the Jet Propulsion Laboratory in 1944 used nitric acid with aniline fuel.
In Germany from the mid 1930s through World War II, rocket propellants were broadly classed as monergols, hypergols, non-hypergols and lithergols. The ending ergol is a combination of Greek ergon or work, and Latin oleum or oil, later influenced by the chemical suffix -ol from alcohol. Monergols were monopropellants, while non-hypergols were bipropellants which required external ignition, and Lithergols were solid/liquid hybrids. Hypergolic propellants (or at least hypergolic ignition) were far less prone to hard starts than electric or pyrotechnic ignition. The "hypergole" terminology was coined by Dr. Wolfgang Nöggerath, at the Technical University of Brunswick Germany. 
Hypergolic rockets do not need an ignition system, so they tend to be inherently simple and reliable. While the larger hypergolic engines used in some launch vehicles use turbopumps, most hypergolic engines are pressure fed. A gas, usually helium, is fed to the propellant tanks under pressure through a series of check and safety valves. In turn, the propellants flow through control valves into the combustion chamber. They ignite instantly on contact, without any risk that a mixture of unreacted propellants might build up and ignite in a potentially catastrophic hard start.
The most common hypergolic fuels, hydrazine, monomethylhydrazine and unsymmetrical dimethylhydrazine, and oxidizer, nitrogen tetroxide, are all liquid at ordinary temperatures and pressures. Thus they are sometimes referred to as storable liquid propellants. They are suitable for use in spacecraft missions lasting for years. In contrast, liquid hydrogen and liquid oxygen are both cryogens whose practical use is limited to space launch vehicles where they need be stored for only a short time.
Because hypergolic rockets do not need an ignition system, they can be fired any number of times by simply opening and closing the propellant valves until the propellants are exhausted. This makes them uniquely suited for spacecraft maneuvering. They are also well suited, though not uniquely so, as upper stages of space launchers such as the Delta II and Ariane V that must perform more than one burn. However, restartable cryogenic (oxygen/hydrogen) rocket engines do exist, notably the RL-10 on the Centaur and the J-2 on the Saturn V.
The earliest ballistic missiles, such as the Soviet R-7 that launched Sputnik-1 and the US Atlas and Titan-1, used kerosene and liquid oxygen. The difficulties of storing a cryogen like liquid oxygen in a missile that had to be kept launch ready for months or years at a time led to a switch to hypergolic propellants in the US Titan II and in most Soviet ICBMs such as the R-36.
But the difficulties of such corrosive and toxic materials, including leaks and explosions in Titan-II silos, led to their near universal replacement with solid-fuel boosters, first in Western submarine-launched ballistic missiles and then in land-based US and Soviet ICBMs.
The trend among western space launch agencies is away from large hypergolic rocket engines and toward hydrogen/oxygen engines with higher performance. Ariane 1 through 4, with their hypergolic first and second stages (and optional hypergolic boosters on the Ariane 3 and 4) have been retired and replaced with the Ariane 5, which uses a first stage fueled by liquid hydrogen and liquid oxygen. The Titan II, III and IV, with their hypergolic first and second stages, have also been retired. Hypergolic rockets are still widely used in upper stages when multiple burn-coast periods are required.
Although not hypergolic in the strict sense (but rather pyrophoric), Triethylborane, which ignites spontaneously in the presence of air, was used for engine starts in the SR-71 Blackbird and the F-1 engines used in the Saturn V rocket.