A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission or a combination of fission and fusion.
In the event of a zombie outbreak, the government may attempt to stop the spread of the outbreak through the use of nuclear weaponry as seen in World War Z, where Pakistan and Iran destroyed each other.
The first part of a nuclear explosion effective against the undead is the initial blast. The heat will incinerate anything in its blast radius. The following shockwave will have mixed results; it will break some bodies or simply knock over others. Radiation and fallout will hamper the lives of survivors in the area. Zombies may be affected by the radiation, and can have the side effect off walking through the contamination zone and surviving long enough to spread the radioactivity further. Radiation will affect the area for decades, or even centuries afterwards.