The steady state model was proposed by three individuals in 1948, Hermann Bondi, Thomas Gold and Fred Hoyle. It is based on the assumption that on the large scales the universe is completely homogenous; that it looks the same from anywhere in the universe at any given time. At the time, this theory wasn't quite as crazy due to our lack of understanding of the universe. The more that we've learned about the universe over the past half century, the more likely that the steady state universe theory is just plain wrong.
The idea of the steady state model was to account for some of the problems that were considered from the Big Bang model: the fact that the universe was calculated to being younger than the solar system was a big problem with the Big Bang model in 1948. The issue back then was that the cosmological constant was much, much higher back in 1948 than what it has been calculated now, the very recent Planck mission getting ~67 km/s/Mpc or the ~72 km/s/Mpc from the WMAP mission data. The very original cosmological constant was calculated by Hubble to be on the order of 500 km/s/Mpc, even after more accurate results had been taken. In 1948, it was still MUCH higher than what we know to be true today. Like several of the other theories that were considered at the time, the steady state model actually fixed some issues with the Big Bang model of the time.
There were a few reasons why the steady state model was eventually discontinued, and one of the reasons was not scientific at all, but purely philosophical. The idea of having a universe that always existed didn't sit too well with many people as it went against creationist beliefs; that the universe had no beginning and always existed. Although this isn't suggesting that the church was beating down on scientists like they did in centuries earlier, this was just a feeling amongst the different scientists.
The last comment means that there should be both old and new galaxies together at the same time, but this is not what we observe when we look out into the universe. The Big Bang model states that in the early parts of the universe, the density was much higher, whereas the steady state model means that the universe today should look more or less identical to what it did 13 billion years ago -- it has always looked the same and will always continue to remain the same.
Throughout history, many different theories have been proposed to explain different phenomenon, some far more outlandish than others. The steady state model was just one of the many theories that have been proposed in the last century to explain where the universe came from and where it is heading. Looking back with the information we know now, it can sometimes be hard to believe that theoretical models such as these could have ever been thought of, as they're so far from the truth. To put this into practice for what we know now, string theory is a great example. String theory is a way in which many scientists are trying to unify general relativity and quantum mechanics, and in a few decades, we may all either be looking back at string theory as being the hard truth, or some crazy idea and exclaiming "What on Earth were they thinking!"