Everything that remains of the star is crushed down into an incredibly small, dense object. Close to the object, gravity is so strong that nothing can get away, not even light. This means that we cannot see anything within that region - hence the name black hole.
That said, it is possible to see the effects of a black Hole on the stars and material around it. Gas, dust and other stars close to a black hole can be sucked in by gravity - a bit like water going down a plughole. As material swirls around the black hole it crashes into each other, producing heat and light. Because this happens away from the black hole, the light can escape so that we can observe the activity.
Once established, black holes can grow by consuming material, stars and even other black holes around them. Over time, super-massive black holes can develop, and it is thought that these lurk at the centre of galaxies.