Poison will last several turns and reduce a percentage of your health every turn. You can cure it with an Antidote potion or with skills that remove poison. You will typically be poisoned by Earth enemies.

Burn will last several turns and reduce your health each turn. You can cure it with Le Water Potion or with some skills that cure burn. You will be continuously burned by Fire enemies, so watch out in those Fire chapters.

Corrupt functions quite differently from poison and burn. Corrupt will last several turns, but it will deal damage to your health only on the last turn. So you better cure it with a Clarify potion or by using a skill that removes corruption before the damage hits you. Corrupt is inflicted by some Dark enemies, so be prepared in those Dark dungeons!

Your hero can also be Frozen by some water enemies. Freeze will last several turns, and while your hero is Frozen, it can not attack or use skills. You can cure Frozen with a Heat Potion.

When your hero is Silenced it can attack, but it can not use its skills. Silence lasts several turns. Silence is often cast by Dark enemies. You can remove Silence by using an Enchanted Water potion.

When the enemy Stuns you, all the heroes of one element will be affected for several turns. Stunned heroes can not attack or use skills. You can remove Stun with a Stimulant potion.

Potions:

Antidotes remove Poison
Le Water Potions remove Burn
Clarify removes Corrupt
Heat Potions remove Freeze
Enchanted Water removes Silence
Stimulants remove Stun
Purify removes any negative status effects e.g. when a monster casts a spell that lowers your DEF or REC

Also:

Healing potions increase your health
Star potions give you skill energy
Steelskin potions increase your defense so enemies do less damage
Strength potions increase your attack"