Once your egg has turned into a chrysalis and hatched into a Moth you will have a new addition to your flutterpedia! You will also get flutterpedia points for hatching new Moths!
To fully fuse and level up a Moth you will need to hatch the same butterfly 5 times - and fuse them together, and feed them the required amount of pollen until they glow blue!
Once they have been fully fused you will get a maximum coin harvest amount, and be on your way to completing an entire set.