If Burmy is Male, it will evolve into Mothim at Level 20.
If Burmy is Female, it will evolve into Wormadam at Level 20.
Burmy's cloak changes depending on where it last battled:
Plant Cloak: if it last battled outside or in tall grass.
Sandy Cloak: if it last battled in a cave, on a beach, or faced a Pokémon from a Honey tree.
Trash Cloak: if it last battled in a building.
As Burmy, the cloaks are nothing but a fashion statement. At level 20, it will evolve into Wormadam, and depending on the cloak, will be part Grass, Steel, or Ground along with it's Bug Type.
Plant Cloak = Bug/Grass.
Sandy Cloak = Bug/Ground.
Trash Cloak = Bug/Steel.