What are all the status effects and what do they mean?

Solution 1:

• Snared: Your character is slowed down. The magnitude of the slow effect varies depending on what's doing the snaring.

• Rooted: Unable to move from your current position.

• Attack Slowed: You swing your weapons more slowly.

• Chilled: Snared + Attack Slowed

• Frozen: Mostly the same as stunned, but certain skills, like the Wizard's Frost Nova's Shatter Rune, cause frozen enemies to behave differently. Frozen enemies leave no corpse.

• Immune: Immune to whatever status effect you're trying to apply. This can be knockback, stun, snared, or any other status effect, depending on the individual in question. Bottom line - one or more of your status effects isn't "sticking", so to speak. Unlike Diablo II, no monster in Diablo III is supposed to be immune to a damage type (though they might have high resistances).

• Knockback: Physically moves the target away from the origin of the attack.

• Stunned: Rooted, and unable to attack.

• Charmed: Fight other monsters instead of the player

• Feared: Running in fear, unable to take action or control direction of movement.

Solution 2:

[RavenDreamer's answer] was fairly complete, but I would add two additional status effects detailed in the wiki.

Confusion : disorients the target, making them unable to tell friend from foe.

Fire DoT : A fire damage over time is a critical effect from a fire-based attack, and will cause damage over time. A target with a fire DoT is easy to see, as it will literally be on fire.

It's not clear from the wiki if these status effects can be generated by monsters or only by player characters, but it seemed most appropriate to add here.

Solution 3:

I would like to add that monsters can sometimes be completely immune to any attack. In that case you have to kill them indirectly:

shield: immunity is temporary, wait 5 seconds until it dies out.

invunrable minions: kill the leader, his minions will die with him.