Creatures are probably the most common spells and permanents (except lands) played in the game. The creature card is used to summon Creatures to take the offense and reduce your opponent's life points by attacking. Creatures can also be used for blocking to prevent your opponent's attacking creatures from dealing damage to you, and they may also have special abilities.
The box with two numbers in the lower right corner of a creature are its power and the toughness. The number to the left of the box is the creature's power, which tells you how much damage that creature deals. The number to the right, its toughness, is how much damage the creature can take before it's be destroyed.
In the first turn that you cast a creature it suffers from Summoning sickness ( it can't attack or use tap abilities), though in your next turn Summoning sickness wears off. A creature with Summoning sickness can still block if it is untapped. The Haste ability allows creatures to attack or use activated abilities the turn they are played.
There are special creatures that are also artifacts, which are called called Artifact Creatures. They are affected by anything that affects creatures and/or artifacts. They can also have abilities.
There are certain creatures that are represented by tokens, called Creature Tokens, these are treated the same as creatures. Tokens in a game are often represented by a facedown card or there are also token creatures such as soldier. They can range from small 1/1 creatures, to large, expensive creatures, such as Outland Colossus.
Tokens go to the graveyard as do regular creatures, and are removed as a "state-based effect" when a player gets priority again. They stay in the graveyard long enough to trigger abilities, like the one of Malakir Cullblade, before they are removed. Whenever a token creature leaves the battlefield, it immediately ceases to exist.
In casual play, people generally don’t bother putting the token (coin/piece of paper/dice) in the graveyard because it’s removed right after, but it’s supposed to be put in the graveyard. Read more about this and other State-Based Effects in the Comprehensive Rulebook, section 420.
Tokens are owned by the under player under whose control they entered the battlefield.
There are many types of creatures. Look just below the picture, and it will say, "Creature - " and then a creature type. Common creature types are Humans, zombies, Merfolk, and birds. Some VERY powerful creature types are Eldrazi, angels, dragons, Shapeshifters, and wurms. They usually have common abilities such as Flying, which can be common but extremely dangerous. Dragons, aven, birds, and angels almost always have Flying. These creatures do not necessarily have large power or toughness, but they can have deadly abilities.