Monsters sometimes come with buffs on them after Trial Forest. When they do, the have an aura on them and the buff written above their heads. They may have more than one buff (highest I've seen is 3). Bosses cannot have buffs.
List of known buffs and effects:
Increase Power: Doubles the damage the monster does. Nothing special, just knock it until it's dead.
Increase Defense: Halves the damage done to the monster. Causes it to delay you and possibly give time for others to gang up on you.
Recover: The monster gets back up instantly after getting knocked down. Pretty useless and actually useful when hitting it with an archer, but running away from that monster will be harder.
Restore HP: The monster recovers HP at a medium pace. Kill it ASAP, you don't want it getting back to full health from critical in a minute.
Super Armor: The monster cannot be knocked down, frozen, petrified, stunned or paused during skill usage. Pretty much immune to everything except damage and death. Extremely deadly when put together with other buffs like Restore HP and Petrify.
There is a bug on Elite Anmon Scouts with Super Armor in Gaikoz's castle - if they try to fall off a platform, they get frozen in place. Also works with Drillmon, Anmon Guard, and the Elite Anmon Guard. Odd that it doesn't bug on normal Anmon scouts though...
Petrify: Causes Petrify when the monster hits you, same effect as the mage's Stone Curse in PvP. You cannot be hit while petrified, but will lose some hp when you unpetrify. If the monster's attack is high, unpetrifying will cause TONS of damage. Dangerous on ranged attackers and high attack monsters.
Cursing: Causes Curse when the monster hits you which lasts for around 10 seconds. You turn a darker shade and lose 1hp everytime you press the z button while still attacking. Either dash attack, use skills or stay away unless you want to drop your hp to the pits.
Freezing: Causes Freeze when the monster hits you. You lose HP gradually when frozen and are stuck in place. You can get hit while frozen, and if the monster freezing you is a fast attacker (or there are many freeze monsters around) you can get stuck in perma freeze and get killed. Deadly in mobs and ranged attackers.