Fragmentation

Often, when we look out into space, we see clusters of young stars. These seem puzzling at first - why would so many stars form in the same area? Isn't there a limited amount of stuff available to form stars in a given region?

The answer has to do with the way that stars form. It all starts with a cloud of interstellar medium. The two main forces acting on it in bulk are gravity, which tries to pull all the mass of the cloud inwards towards the center, and temperature/pressure, which tries to push the cloud outward, preventing its collapse. For a cloud to collapse, then, its mass needs to exceed a critical mass, called the Jeans mass, after Sir James Jeans OM FRS MA DSc ScD LLD (this guy had a lot of titles). The Jeans mass is a function of the density, mass, and temperature of the cloud. A cloud with more mass will collapse. A cloud with less mass won't.
To understand why a cloud can form clusters of stars instead of just one, we need to take a slightly closer look at what the Jeans mass really says. I won't go into the math here, but conceptually, all else being equal, an increase in the temperature of the cloud will mean it takes more mass to overcome the warmer material pushing outward. More subtly, an increase in the density of the cloud reduces the Jeans mass, essentially because gravity has an easier time bringing everything together.
Suppose that we have a cloud with sufficient mass to begin collapsing. As the dust and hydrogen collapses inwards, the density naturally increases. But the extra energy the atoms gain is predominantly radiated off, and the cloud isn't dense enough to be opaque, so the energy doesn't go into the cloud. This means temperature stays roughly constant at the start of collapse. Because of these changes, the Jeans mass drops, and suddenly a whole bunch of regions of the cloud have the necessary mass to collapse in on themselves. Because the cloud cannot possibly be completely homogeneous, little pockets of collapsing dust form in a process called fragmentation. These will eventually become the young stars we can observe in a cluster.

Why, you ask, does the fragmentation stop? Why doesn't the cloud just keep dissolving into smaller and smaller bits of collapsing material? That's because eventually, the collapsing regions' density increases enough to start absorbing their own radiation, which causes the temperature of the protostar to rise, and cancels out the density effect.