Boost Material Monsters are monsters that provide a large amount of experience for boosting a monster.
There are 4 types of Boosters which are Caterpillars, Cocoons, Moths and Super Moths. There is one of each type for every affinity except Prismatic.
Caterpillars give 2,000 XP when boosting (3,000 with affinity boost), Cocoons give 5,000 XP (7,500 with affinity boost), Moths give 10,000 XP (15,000 with affinity boost) and Super Moths give 30,000 XP (45,000 with affinity boost.)
Caterpillars, Cocoons and Moths all appear in the Lucky Zone and all 4 types appear in certain levels of the weekly Event.