We know that the Earth is one of several planets orbiting the sun, the sun is one of billions like it in the Milky Way , and the Milky Way is a typical large galaxy of the sort we see in every direction when we look out into the far universe. The conjecture goes a step further and assumes that the Milky Way's neighbourhood in the realm of galaxies is quite ordinary, neither unusually crowded nor particularly deserted. When we look at anything, we see it, not as it is now, but as it was when the light left it. The usual cause of such a redshift is the Doppler effect , and by assuming this it is possible to calculate the recession velocity of the galaxy. This expansion is quite a subtle concept.
Expansion means that the distance between any two particles is getting larger.
Within these objects the original expansion has been overcome by gravity. This is a runaway process. Its gravity will slow down both its own expansion and that of surrounding matter, so both the size of the region and its relative over-density increase. Eventually the expansion near the centre is stopped altogether. The size of the region affected continues to grows as outlying particles have time to move in.