From Nookipedia, the Animal Crossing wiki
The Bagworm (ミノムシ, Minomushi) is a common insect that first appeared in Animal Crossing, then is absent in Animal Crossing: Wild World, but reappears in Animal Crossing: City Folk and Animal Crossing: New Leaf. It appears throughout autumn and winter and can be shaken out of trees. Upon shaking, it dangles from the tree for a few seconds before disappearing back into the tree. The tree can be shaken repeatedly if the Bagworm is not immediately caught. In Animal Crossing, Bagworms do not crawl back into the tree after being shaken, unless the player leaves the acre. Bagworms are quite common. In Animal Crossing: New Leaf, Bagworms do not spawn if the gate is open.
If a Bagworm is released, the casing bounces to the floor and disappears.
Upon Donation to the Museum
In Animal Crossing"The bagworm is not a worm per se, but rather any moth of the family Psychidae while in its caterpillar phase. Bagworms construct their cocoons by cutting leaves or branches to the length of their own bodies. Next, they hang these leaves or branches on shrubs or trees and spin their cocoons around them. Fascinating! Interestingly enough, only males of the species become moths. Females spend the rest of their lives in the cocoons. The black, furry males fly from cocoon to cocoon, leaving the females to lay 500 or more eggs, than die. Just imagine it! 500 or more eggs! And than they die! That's not very sporting, if you ask me. Not at all! I can't see any female owls standing for that nonsense. My dear old mum would have given my da an earful, wot! In any case, where was I? Ah, yes. Bagworms, bagworms. Quite the pests, they are...Voracious in the extreme! An infestation of bagworms can defoliate entire trees in surprisingly rapid fashion. Gluttonous monsters! This is particularly harmful, sometimes fatality so, in evergreens, whose needles are never replaced. Hundreds and hundreds of bagworms...eating and eating...stuffing their bug-gullets...Blech! Wretched villans!"
In City Folk
Blathers will say this after taking the Bagworm:
"In time, a bagworm transforms into a bagworm moth, eh wot? The bagworm's casing is really rather unfashionable, bordering on hideous. Ah, but by sticking wool threads into the bagworm's casing, you can make a little 100%-wool coat for it! Of course, that would be mad. And inside that wool coat would be a big moth, which no one needs..."
Once donated, Bagworms can be found in the upper left corner of the insect room in the museum, hanging from a tree.
Bagworms can be found around the world- there are around 600 known species. The casing of the bagworm serves to protect and camoflage the larvae until it emerges as a moth.