Quick explanation
A gamma-ray burst is the most energetic explosion in the Universe; in a few seconds they can emit as much energy as our Sun will do during its entire life of 10 billion years.
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Gamma ray bursts (GRBs) are short-lived flashes of gamma ray photons, the most energetic form of light.
Lasting between a few milliseconds and several minutes, GRBs shine hundreds of times brighter than a typical supernova. That means that for every second that a GRB lasts, it will produce as much — or even hundreds of times as much — energy as our Sun will do in all its lifetime of 10 billion years.
GRBs were discovered serendipitously in the late 1960s by U.S. military satellites looking out for Soviet nuclear testing in violation of the atmospheric nuclear test ban treaty. At first, astronomers did not know whether the sources were in the distant Universe, in our own Milky Way, or even inside the Solar System. However, now we know that they all lie at cosmological distances, billions of lightyears away. This means that the light we see has been traveling for billions of years, so that in fact we are looking billions of years back in time, when the Universe was still young and the first galaxies had just formed (although the closest GRB observed was only about one billion lightyears distant).
Although most details of the mechanisms underlying this fabulous phenomena are still quite uncertain, two different scenarios are believed to be the progenitors of the GRBs, depending on whether it is a long (> 1 s) or a short (< 1 s) GRB:
Long GRB — explosion of a massive star
When a very massive star, perhaps more than 40 Solar masses, ends its life, it explodes in an extremely powerful supernova, a so-called hypernova. If the dying star is rotating rapidly, a torus is created around its equator, collimating the exploding material in two jets along its axis of rotation. If furthermore the star is of low metallicity, i.e. has very little elements other than hydrogen and helium, the outer layers has been stripped off, allowing the jets to reach the surface and travel outwards with 99.995% of the speed of light. The gamma rays are created when the shock wave collides with stellar material still inside the star. Meanwhile, the inner core collapses to a black hole.
Finally, if we happen to be in the direction of one of the jets of this magnificent collapsar, as it is called, we will observe it as a gamma ray burst. Also, softer radiation is produced, resulting in the so-called afterglow of progressively less energetic photons, starting with X-rays, followed by ultraviolet, visible and infrared light, and eventually radio waves. The afterglow phase can last for days or even weeks.
Short GRB — collision of compact objects
For the short GRBs, the story is thought to be quite different. Most stars are in fact two (or more) stars in orbit around each other, a so-called binary system. If both stars are massive enough, they will end their lives as neutron stars or even a black hole. The two compact object will continue their spiralling, but gradually lose energy due to emission of gravitational waves, thus approaching each other, getting closer, closer, closer, before finally tidal forces rip the neutron star(s) apart, and the the two objects merge into a single black hole after releasing a tremendous amount of energy.