A good example of a star nursery is once again in the constellation of Orion. If you look at Orion's sword, you will see that the middle star appears misty. This is M42 - the great Nebula in Orion , one of the most famous and most photographed objects in deep space. This is but one example of a star nursery. Our own sun was born out of a cloud of dust like this.
Most stars live the main part of their lives as main sequence dwarfs.
For example, Alpha Centauri can go on, as a main sequence star for another 10 billion years until eventually, it will grow warmer and brighter as it consumes all the hydrogen in its core. Now it is no longer a main sequence dwarf, but becomes a red giant. Then it fades away again so that only a telescope can see it. The core will fade away as a white dwarf. Eventually this cloud of dust or Nebula, will be all that remains of the star - like a celestial graveyard.