This was a cosmological model postulated in 1948 by astrononomers Fred Hoyle, Hermann Bondi, and Thomas Gold to explain the origin of matter in the Universe, as well as the expansion of the Universe demonstrated by Edwin Hubble.
According to this theory, hydrogen forms spotaneously in the voids between galaxies as they move apart. The model assumed that the Hubble Constant was a true constant in space and time, and produced a Universe whose average matter density was always the same. The actual mechanism of formation was never explained. In some versions of the theory, the Universe is infinitely large and infinitely old.
In a way, the steady-state theory was a bit of wishful thinking on the part of its proponents, part of a long string of theories designed to avoid the unappealing universe which dies out as it expands forever. Unfortunately, Nature is not swayed by our aesthetic judgements.
On the other hand, the steady-state universe fit with the available data at the time, and gave the prevailing explanation of the Universe's expansion, the Big Bang, a run for its money. In fact, Hoyle himself coined the term "Big Bang" in an attempt to disparage the George Gamow theory he found so repugnant. At the time, there was no evidence that the Big Bang was any more "real" than the Steady-State Universe. So for a while, the two theories earned equal time in popular discussions of cosmology, and professional astronomers didn't categorically rule it out.
But when the cosmic microwave background radiation was discovered in 1965, most astronomers rejected the steady-state universe in favor of the Big Bang. A cosmic microwave background is evidence for a "beginning event" such as the Big Bang, or at least a period when matter and energy were so dense that radiation dominated the Universe. A temperature of 3o K argues for a much younger Universe than Hoyle, Bondi, and Gold's equations could produce.
Hoyle, of course, never gave up on his theory, finding a way to adjust it to create a cosmic microwave background, but he was just as devoted to his theory of panspermia, and astronomy had moved on by that time.
If you would like to see some of the math behind the steady-state universe, you can visit http://scienceworld.wolfram.com/physics/Bondi-GoldSteady-StateCosmologicalModel.html