A star cluster is a clump of stars that are formed roughly at the same time.
There are basically two different kinds:
Globular clusters are compact, spherical clumps of old and hence yellow-/reddish stars.
Open clusters are more diffuse clumps of young and hence more bluish stars.
A globular cluster is a spherical clump of stars, formed at about the same time. Most globular clusters are very old, formed in the early age of the galaxy. Because they are so old and there is no more gas left to form new stars, all the massive stars — which burn their fuel quickly and with a bluish color — are dead; only the light and yellow/reddish stars are left, giving the globular cluster its color.
When a spiral galaxy was young, it hadn't yet flattened to form its disk; for this reason globular clusters in a spiral galaxy like the Milky Way do not lie in the galaxy's plane, but instead in a more spherical halo around the galaxy.
Over time, globular clusters have become gravitationally very tightly bound, giving them their spherical shape. Whereas the distance between stars in the Sun's neighborhood is typically around 4 light years, the stars in the centers of globular clusters are 100 to 1000 times closer.
There are about 150 known globular clusters in our galaxy, the Milky Way, with perhaps 10-20 pieces yet to be discovered.
See my own observations of globular clusters here.
Open star clusters are much smaller than globular clusters; typically they consist of a few thousand stars. Since they are not so tightly bound by gravity, they dissolve after a few tens to hundreds of millions of years.
That is, an open cluster still has its massive stars, which shine blue and bright. Sometimes, the stars are still in the gas sky they were born in, and this cloud is lit up by the stars. Therefore, open clusters are sometimes seen enshrouded in blue, diffuse nebulae.