Two theories try to explain the origin of the Universe. In the Big Bang theory, all the matter and space in the Universe began in a single, extremely hot and dense point about 13.8 billion years ago, and has been expanding ever since. In the Steady State theory, the Universe has no beginning and no end. On a large scale it always looks the same, with the same average density of galaxies at all times.
Both theories say the Universe is expanding, so both can explain red-shift. As space expands, galaxies move apart and the light from them is stretched to a longer wavelength. The further away a galaxy is, the faster it moves away, so the bigger its red-shift.
The theories differ over what happens to the density. In the Big Bang theory the same matter is spread through a bigger and bigger volume, so the density of the Universe decreases over time. In the Steady State theory the density stays constant, because new matter is continuously created in the gaps between galaxies as they move apart.