Moth

The Moth is a nocturnal insect, that can be found on cloudy nights. Players seem to detest them even more than cockroaches. Moths are usually found by bright lights.

In City Folk
"Many people hate moths, yet love butterflies, but the truth is that both belong to the order . Since both are covered in unspeakable veins and foul powder, I suggest they are equally distasteful."

The moth can be found in the upper-left hand corner of the insect exhibit, flying around a lamp near the bagworm.

In New Leaf
Upon being donated, the moth can be found in the room of the bug exhibit with the light in, flying around the light. The exhibit has this to say about the Moth:

"Moths are related to butterflies, but they're most often active at night instead of day. They use their large antennae to sense, smell, and guide themselves in the dark. Interestingly, the number of moth species is estimated at 160,000, so "moth" is a fairly broad descriptor."

Encyclopedia Information
When the player has caught a moth, they can find information about the insect in the bug menu. Below is the information regarding the moth: