Character Tokens were introduced with the 0.6.0 update. You could originally only obtain Character Tokens by levelling up or buying them from the Store, but the 3.0.0 update made them more accessible and also introduced multiple tiers of Character Tokens: Common Tokens, Uncommon Tokens, Rare Tokens, and Epic Tokens. Each of these tiers will yield only Characters that have a rarity higher than or equal to the type of token. So:

Common Tokens will yield Common, Uncommon, Rare, and Epic Characters

Uncommon Tokens will yield Uncommon, Rare, and Epic Characters

Rare Tokens will yield Rare and Epic Characters

Epic Tokens will yield Epic Characters

You can spend your Character Tokens by going to the Token Machine, where you can obtain token-based Characters.

You can obtain Tokens in the following ways:

Leveling up. Odd numbers will not give you any Character Tokens (only Coins), whereas even numbers will give you both Character Tokens and Coins.  To see the specifics of what you get, click here.

Spinning the Common/Daily spin. When spinning the Common/Daily spin, you have a chance of receiving one of the following Gems rewards:

1 Common Character Token

Buying with Gems. In the Shop, you are able to purchase Tokens with Gems for the following prices:

1 Common Character Token - 65 Gems

5 Common Character Tokens - 275

10 Common Character Tokens - 500

1 Uncommon Character Token - 150 Gems

5 Uncommon Character Tokens - 650 Gems

1 Rare Character Token - 325 Gems

5 Rare Character Tokens - 1.400 Gems

1 Epic Character Token - 700 Gems

5 Epic Character Tokens - 3.000 Gems