Upgrading Corpse Explosion increases the Poison from 6 (21 total damage) to 9 (45 total damage).
Corpse Explosion is an exceptionally strong card when fighting multiple enemies. Even without the above-average amount of Poison, it can inflict massive amounts of area-of-effect damage and easily clear boards.
The "death explosion" effect lasts indefinitely, and doesn't require the fatal damage to come from Poison. Even better, it can stack, allowing an enemy to deal two or more times its max HP to all foes.
Because the poison and explosion damage is dealt after Block is removed, very few enemies can block it.
As a Poison enabler, it's strong but clunky. 9 Poison is the single largest printed amount of Poison, but two Energy is a big investment. Consider it a step up from Bouncing Flask in most situations.
A key decision when casting Corpse Explosion is whether to target an enemy with low HP to wipe it off the board earlier, or to target the enemy with the highest max HP to wipe the entire board at once. Generally, targeting the beefiest enemy and then focusing all of your attacks on it is the optimal play, though if a shuffle is imminent, it may be smarter to pick a weaker enemy and try to stack the effect again.
Corpse Explosion is an excellent workhorse for defensive decks. The Poison cuts through Block while the explosion scales the damage up, allowing you to fully focus on defense.
Upgrading Corpse Explosion is recommended to increase its potency against single enemies.
Burst allows Corpse Explosion to apply a huge amount of Poison and area-of-effect damage.
Corpse Explosion triggers Sadistic Nature twice.
This card is most likely a reference to the Diablo II Necromancer Corpse Explosion ability; in addition to have the exact same name, the mechanics of the card are also the same (deal damage to other enemies based on the health of the target)