Petrification is a powerful debilitation that slowly impedes the Arisen or pawn's movement before turning them to stone, and then killing them.
When afflicted, the player will slowly start to have all forms of movement hampered, and after 40 seconds will turn to stone and be rendered immobile. If an Arisen is completely turned to stone, he/she will immediately break and die (though you can still be revived with Wakestone). If a pawn is turned to stone, you have a set amount of time to cure them before they break and die - once a pawn dies from petrifaction it cannot be revived, and is returned to the rift.
Petrification is easily one of the most dangerous status ailments in the game, and the hardest to cure. High Halidom and common medicines cannot cure it, and it's uncommon nature may take you by surprise.
The only way to cure petrification is through use of a Secret Softener, Cockatrice Liquor, Panacea or by having a Sorcerer cast High Voidspell. It is important to note that when trying to cure pawns you should give them a Softener or Panacea before they become completely petrified, or they will not be able to use it - the only way to cure them then is by using a Cockatrice Liquor or Ne'er do Part. The Sorcerer spell High Voidspell can also remove petrification.
Enemies that can cause petrification include: Cockatrices, Gargoyles, Lichs, Evil Eyes, Vile Eyes, Gorechimeras and the Ur-Dragon; Arisen and Pawns can also inflict petrification using either the Petrifaction Archmagick or Petrifaction Arrows. Cockatrices and Gargoyles particularly will use Petrifaction as one of their main weapons, so you should bring status protection such as Sobering Wine or the cures mentioned above before facing them. Petrification is a likely risk when exploring Soulflayer Canyon and post-game The Everfall, so be prepared before entering these areas too.
It should also be noted that the full set of the abbysinal armor can raise your resistance up to 100% which means you will be immune to any kind of petrification at all