There are two types of tans: Tans and Kingtans.
Tans
Normal Tans can be exchanged at the Monster Exchange at a 5:1 rate for a Kingtan of the same color. They provide no other use.
Kingtans
Kingtans will increase the Skill Up rate of skill-up fodder (cards with same active skill) to 100%. Do not confuse these with Pys, as they will not increase the number of skill-ups gained from them.
DO NOT USE KINGTANS TO SKILL UP WITH DUPES OF REM CARDS.