A galaxy cluster is a moderately large group of galaxies, generally no more than 1,000 total, which are associated either by gravitational attraction or because they simply formed alongside each other. Often, galaxy clusters will have very large elliptical galaxies or spiral galaxies at their center, around which the others orbit.
There are millions of galaxy clusters in our universe, and most of them are collectively bound into even larger structures called superclusters, filaments, or great walls.
As universes expand, it is likely that only the densest of galaxy clusters will stay together and eventually coalesce into enormous elliptical "supergalaxies" which will then slowly die out.