It disables it. When you "punch holes" in a missile with a conventional warhead, it explodes or it flies off-coarse and lands somewhere other than where it was aimed.
With a nuke warhead, one hopes that the device is disabled and it falls to the earth and does not perform it's intended function.
Worst case: the warhead works as designed and a thermonuclear detonation occurs.
Next worse case: The conventional explosives in the warhead detonate but nuclear fission does not occur. Radioactive material is spread over a wide area. (A dirty bomb.)
Best case: The device is disabled and falls to the earth causing little or no damage and contamination.
I'm a Bible-believer and believe Damascus will be destroyed in the future. Wouldn't it be just a tad ironic if Ahmadinejad's missile did it?
Wouldn't the best-case scenario be, if Iran launched nukes at Israel, to detonate their own missles over their own territory? How ironic that would be. And sublime justice.
It'd be a real shame if all of Iran's missiles fired towards Israel were shot down over Syria. ;-)