A white dwarf is the remnant core of the star after it has expelled its envelope as a Planetary Nebula.  Earlier, in between fusion stages, the core had contracted before the next element started fusing.  The result is that the core is now only about the size of the Earth, yet contains about half the mass of the Sun!  As a consequence, it is extremely dense.  A teaspoon of white dwarf material would weigh roughly a ton on Earth.  It is dead in the sense that no further fusion will occur.

 

What holds it up if there is no fusion?  Remember that it now consists mainly of the nuclei of carbon and oxygen atoms as well as electrons.  The density is now so high that the electrons are so close together that they resist further collapse and can balance the gravity of the star.

 

The picture below is a Hubble Space telescope image of the white dwarf in NGC 2440. This remarkable image still shows both the planetary nebula (the ejected outer layers) as well as the dense core, the white dwarf (Click the image to enlarge it.).

The images below that show a dense cluster of stars called a Globular Cluster.  These contain many white dwarfs, and the blow-up on the right identifies some of them.