A token is a permanent that is not represented by a regular card with a casting cost.   Richard Garfield created tokens for Alpha, as opposed to counters, to make The Hive possible.  Usually, but not always, tokens are creatures.
Normally tokens can exist only on the battlefield. If a token leaves the battlefield and goes to another game zone, it can't change zones again, and it will be there only briefly before ceasing to exist as a state-based effect.
There were so many cards in Fallen Empires that produced tokens and/or required counters that Wizards of the Coast issued a cardboard sheet of them in Duelist #4.  Special token cards were first printed for Unglued.  Unglued's tokens proved so popular they spawned the new tokens given away in the Magic Player Rewards program.  Since Tenth Edition they appear as marketing cards in booster packs.
Examples and rules
Token specific creature types
Some creatures named in the legal subtype-list only appear on tokens.
- Camarid tokens are created by Homarid Spawning Bed and Sarpadian Empires, Vol. VII.
- Caribou tokens are created by Caribou Range.
- Citizen tokens are created by Icatian Crier, Icatian Town and Sarpadian Empires, Vol. VII.
- Deserter tokens are created by Kjeldoran Home Guard.
- Germ tokens are created by living weapons.
- Graveborn tokens are created by Balduvian Dead and Sek'Kuar, Deathkeeper. Graveborn Muse doesn't have the subtype Graveborn.
- Orb tokens are created by Phantasmal Sphere. Note that artifacts like Chaos Orb don't have the Orb subtype.
- Pentavite tokens are created by Pentavus.
- Pincher tokens are created by the Summoning Station.  Pincher Beetles doesn't have the subtype.
- Prism tokens are created by Diamond Kaleidoscope, but not by Pentad Prism or Prismatic Circle.
- Reflection tokens are created by Pure Reflection and Spirit Mirror, but not by the Kami of Twisted Reflection.
- Sand (Warrior) tokens are created by Hazezon Tamar and Dune-Brood Nephilim , but for example not by Choking Sands or Sandstorm. Sand Golem is not a Sand Creature.
- Saproling are produced by many green-aligned fungus and/or plant-based cards.
- Serf tokens are produced by Sengir Autocrat.
- Splinter tokens are created by Splintering Wind, but not by Splinter, Splinter Twin or Bone Splinters.
- Survivor tokens are created by Varchild's War-Riders under opponent's control. Note that Auriok Survivors, Riptide Survivor and Survivor of the Unseen don't have the survivor subtype.
- Pink Giant Teddy Bear tokens are created by Water Gun Balloon Game.
- Tetravite tokens are created by Tetravus.
- Triskelavite tokens are created by Triskelavus.
- Comprehensive Token Table - A comprehensive sortable table that lists every possible token that can be generated in Magic: the Gathering, the properties of those tokens, and the cards responsible for their creation (does not include tokens that copy other cards).
- Like for regular cards, the card frame for tokens was updated with Eighth Edition. "Token"now appered in the type line, thought it has never become an official subtype 
- The first non-creature token was the enchantment token copies of Imperial Mask that can be given to your teammates.
- The second non-creature token was the Gold artifact token produced by Gild from Born of the Gods and King Macar, the Gold-Cursed from Journey into Nyx.
- The third non-creature token are the Land Mine artifact tokens produced by Goblin Kaboomist from Magic 2015 Core Set.
- Intangible Virtue is a Lord-type enchantment that gives +1/+1 and vigilance to creature tokens.
- Tokens were featured as rules card 4 of 9 in the Magic 2011 set.
- Saprolings are the token creature type most easily created, 63 unique cards are capable of specifically creating them.
- The first non-copy token with non-keyword rules text was the Tetravite token produced by Tetravus from Antiquities.
- The first non-copy token with an activated ability was the Skeleton token produced by Drudge Spell from Homelands.
- The first non-copy token that could produce another token was the Ooze token produced by Mitotic Slime from Magic 2011 Core Set.
- Because Magic Online needs to represent all the tokens in the game, art needs to be created for even the most insignificant tokens. And for some of that art, Magic Online is the only place it appears.  
- Mark Rosewater. (May 27, 2002.) "Tokens of My Affection", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Mark Rosewater. (May 27, 2013.) "Token of Appreciation", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Mark Rosewater. (September 26, 2005.) "+1/+1 For the Road", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Magic Arcana. (May 31, 2002.) "Fallen Empires tokens", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Magic Arcana. (May 27, 2003.) "Soldier Tokens", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Mark Rosewater. (April 5, 2004.) "Unhinged or No?", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Magic Arcana. (June 01, 2004.) "Pincher token art", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Aaron Forsythe. (January 27, 2006.) "Guildpact: Twenty Questions", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Magic Arcana. (September 24, 2003.) "The new look of tokens", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Magic Arcana. (July 30, 2002.) "Unseen tokens", Daily MTG, magicthegathering.com, Wizards of the Coast.
- Magic Arcana. (May 03, 2005.) "Oyobi Spirit Token Art", Daily MTG, magicthegathering.com, Wizards of the Coast.