The material they make the sabots out of is Depleted Uranium. It's pyrophoric; it catches fire in air. Thus, when it goes through the first set of armour, the sabot disentegrates and catches fire. Aside from horribly burning everyone inside, it uses up all the oxygen, and sets off any ammunition lying around.
You also get a good-size chunk of very dense material flying out the other side.
However, due to political backlash agains scattering slightly radioactive dust everywhere and use of the word 'uranium', people are now using tungsten, which just goes in and takes chunks of the armour with it. These don't set off everything automatically, and so are usually followed up with a HEAT round (High Explosive Anti-Tank), which is a shell designed to send a jet of molten metal (usually copper) through the tank's armour on impact. This is extremely hot, as well as there being a lot of force transferred. This, combined with the already-weakened structure, makes a garaunteed boom.
Incidentally, the words 'uranium', 'nuclear', and 'radioactive' can panic politicians. Go on, try it with your local senator today!
They're also words that can set off government search engines, just like 'dirty bomb', 'assassination', and 'illuminati'.