Teachables are the name for the 3 unique perks that come with each character. By default these perks will only spawn on the Bloodweb of their character.
In order to obtain a Teachable perk on other characters, you have to unlock it by levelling the character to the level of that teachable (level 30, 35, and 40) wherein it will appear on the Bloodweb in a special orange rarity of the perk. Upon buying that special variant, the perk will then be able to spawn in the Bloodweb of other characters.
You can also buy teachables on the Shrine of Secrets when it appears on there. This is handy as it lets you unlock other character's teachables without needing to own the associated character.