General information:

Monsters, or commonly referred to as 'Mobs' are game entities which can be slain in order to obtain Experience points and items.
There are hundreds and hundreds of different monsters in the game of all shapes, sizes and colors. The whole gameplay revolves highly around slaying these monsters, from the early days all up to the end game, many different monsters will have to be slain for goals to be achieved.
They can be spotted on the minimap in the form of a red dot. While in real-time, they can be differentiated from players by usually having a unique model (Be it a little critter or a scary dragon) and they will always display their level and name when hovered over.

Tip: Holding shift down will display all nearby monsters' Hit points and name/level, as if they were hovered over.

The importance of Monsters:
Monsters are important for a few main reasons.
Experience - As mentioned before, killing monsters grants experience. This allows players to level up after having obtained the necessary amount for their current level. Of course, killing monsters isn't the only source of experience, it's the most efficient one.
Items - Nearly all monsters in the game drop up to several items when killed. They generally drop one or two items at a high rate, which are generally considered useless. However, they can be sold to NPCs to earn a little bit of pocket money, and some of them are quest requirements. They drop equipment (which can be really strong) at a lower rate as well.
Quest requirement - Many quests revolve around slaying certain monsters and/or obtaining certain items which they drop.

Monster stats:
Monsters, just like players, have their own stats (Some even have their own unique skills!), with some subtle differences.
General stats - These stats are the exact same as player stats. They have attack, which determines how much they will attack, defense and pr, which determine how much damage they can take, hit rate and dodge, which determine how often they will hit or get it and etc. Monsters have a HP bar as well, where players can track how much more they need to attack the monster before it dies.
Level - Monsters have their own level, higher level monsters naturally drop better treasures and give more experience, but they gain increasingly higher stats as well and/or skills as well.

However, stats unique to monsters are:
Aggravation range - The range at which aggressive monsters will notice a player and move towards them in order to attack.
To better understand this, aggravation, commonly referred to as aggro, first has to be explained. When a monster gets aggravated on a character it will attack it until the player leaves its chase range.
Chase Range - The range which indicates to which point an aggravated monster will keep attacking the player. When it exceeds that range, it will get de-aggravated (de-aggro'd) and return to its original place.

Types of monsters:
The primary differentation between monsters is land/sea. The sea is home to many monsters, many of which drop valuable items for various purposes (Cooking, quests), but it is not a good place for leveling up.
Land monsters on the other hand, do not necessarily drop valuable items. They, however, tend to be killed faster and give the same amount of experience as sea monsters, which makes them better in that aspect.

The second criteria is the aforementioned aggravation (aggro). Based on it, three types of monster can be differentiated.
Passive - These monsters never get aggravated. No matter what the player does to them, they will mind their own business. Few low level monsters fall into this category.
Mystic Shrub
Sleepy Snail

Retaliatory - These monster will ignore the player, unless they get attacked. At which point they will retailate and keep attacking the player until he gets out of their chase range. At which point they will "cool off" and ignore the player unless attacked again. Many lower level mobs fall into this category, but a few strange high level Yetis do as well.
Forest Spirit
Snow Squidy
Rookie Boxeroo
Horrific Snowman

Aggressive - These monsters will attack the player as soon as one walks into their aggravation range. Many monsters, even lower level ones, fall into this category. All bosses and mini-bosses are aggressive as well.
Miner Mole
Skeletal Warrior
Swamp Bog

In order to slay monsters, players must deal enough damage to them and reduce their hit points to zero. As it was said before, hovering over them will display their current hit points and in order to use regular attacks, all that has to be done is click on the monster and the character will start attacking it.
This is one way of engaging "Combat mode" with monsters. Combat mode means that the monster (unless passive) will attack the player until it dies or the player escapes its aggravation range. Aggressive monsters will automatically start hitting the player, hence combat automatically begins as soon as they are aggro'd.

Besides attacking the monster with regular attacks, players can also use harmful skills on them to decrease their HP and ensuring that they meet their end faster.

Special monsters:

Certain monsters which are a bit different. Although the same rules regarding stats and aggravation apply to them, there's a few aspects which makes them stick out.

Mini-bosses - They are an improved version of an already existing monster and tend to have vastly increased stats and drop better treasures. Although there is nothing special to say about them, they deserve a mention.
Little Squidy Captain
Violent Air Porky
Sorrow Archer Captain
Master Swamp Watcher

Bosses - Unlike mini-bosses, these monsters are usually difficult to kill and require team effort. They usually contain valuable treasures as well. The special thing about them is how they are partially immune to certain disables and usually have very high stats and unique skills which makes them all the more difficult to beat. They are mostly located in Mazes or Dungeons.
Death Knight
Huge Mud Monster
Snowman Warlord
Black Dragon

Treasure Chests - Chests are strange monsters which are usually found in mazes, generally guarded by a large number of monsters as the emphasis on their name is on Treasure. They themselves don't attack and have no dodge, which makes them fairly easy to kill, but getting to them may not always be as simple. Generally found in Mazes, Dungeons or other high level areas.
Abandoned Chest 1
Chest of Demonic World 2
Soul Gathering Coffin

Additional information and tips:
-The experience which monsters grant depends on the difference between their and the player's level. The most experience is given when the player is between 9 levels below the monster and 4 levels above.
-Certain monsters are more fit for certain classes. Monster with high def/pr are better for magic classes, while monsters with low dodge and high health are better fit for physical classes.
-When attacked by multiple people, the monster will give more experience to the person who dealt more damage. Altough the one who aggravates it will earn a big portion of the experience.
-When someone uses Heal on a player who aggravated monsters, the healer will aggravate them and get them to attack it instead.
-The sea has Bosses and Mini-bosses as well.