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A Treasure Token is a predefined Token which can be tapped and sacrificed for a single mana of any color.
They are considered Artifacts, so they add to the count if you have something that's counting the number of Artifacts you control. Tokens can't exist anywhere other than the Battlefield, so you can't have a Treasure Token in your Hand, Library, or Graveyard.
However, when a Token is sacrificed or otherwise destroyed, it touches the Graveyard for a second before getting Exiled (and ceasing to exist), so if something cares about an Artifact going to the Graveyard, it will trigger that as well.
What is a Token?
A "Token" is a Permanent that doesn't have an actual card to represent it.
Lots of things create Tokens, and they do not have to be represented by an official Token card. Anything can represent them, from dice and counters to toy trains and stuffed animals. Tokens cannot exist outside of the Battlefield, so returning one to your Hand or Library, or putting into the Graveyard, will automatically trigger a state-based effect which Exiles the Token.
As pointed out above, though, the game will still track a Permanent entering or leaving the Battlefield, and any effect that cares about that will still trigger.
How do I use a Treasure Token?
When using Treasures, you tap one, sacrifice it, and add a mana of any color to your mana pool. The Token touches the Graveyard and disappears forever, because Tokens can't exist outside of the Battlefield.
The longer answer is it's an Activated Ability, but a special one because it's also a Mana Ability.
You pay the cost, which is tapping, then sacrificing, the Token. As a result, you create a Mana of any color and add it to your mana pool, where it will exist until it is either spent or otherwise drains from your mana pool, like at the end of a phase of a turn.
Because it's a Mana Ability, it doesn't use the stack and cannot be responded to.
What is the history of Treasures?
Treasure Tokens were introduced in Ixalan block. Gold Tokens, which are similar but do not require a tap to function, were considered, but Improvise was introduced in the same block.
Improvise is a mechanic that allows a player to tap Artifacts to help pay for Artifact spells, and Gold Tokens proved too powerful (effectively creating two mana - one for the Improvise, another from the sacrifice). Adding the tap required changing the name, and Treasure Tokens were born.
Treasure Tokens were designed to be primarily in Red and secondary in Green; however, Blue got far more than Green in early sets. Black most often requires an additional cost to make Treasure Tokens.
Since Ixalan, they have been in several other sets and are now considered deciduous, which means they can be used when they fit the design but are not required. This is as opposed to evergreen, which are keywords that can always be used and show up in most sets (like Flying or Trample).
Are there other Treasures?
Yes! There are six non-token Treasures.
- Buried Treasure
- Courier's Briefcase
- Dire Mimic
- Glittering Stockpile
- Goldhound
- Mimic
Most of these have the same ability as a Treasure Token: tap, sacrifice, add a mana of any color. However, two of them work slightly differently.
Goldhound is a 1/1 Artifact Creature - Treasure Dog with First Strike and Menace for 
. You can tap it and sacrifice it for a mana, but because it's a Creature, it has summoning sickness, which means you can't do it on the turn it comes into play.
In later sets, sometimes Treasure Tokens enter tapped, which effectively gives them summoning sickness as well - they can't be used the turn they come into play.
Glittering Stockpile is an Artifact - Treasure for 
. You can tap it to add and put a Stash Counter on it, or you can tap and sacrifice it, then add 
mana of any color where X is the number of Stash Counters on it.
So, it functions as a mana rock, but also kind of a treasure chest, where you store up mana until you're ready to use it.
Final Answer
A Treasure Token is an Artifact Token which can be tapped and sacrificed for a single mana of any color. They are created in several ways; are Permanents while they're on the Battlefield, cannot exist in your Hand, Library, or Graveyard; do trigger enters and leaves abilities; and can be represented by anything as long as the state of the board is clear.
