Hi,
I can't tell exactly what insect this is but perhaps an Indian meal moth? You are welcome to bring a sample to the Master Gardener office at the Tolland Ag Center or to UConn's Home & Garden Education Center in Storrs for a positive ID. If it is a meal moth, most likely it came in on some source of grain - maybe cereal, crackers, dog or cat food, bird seed, old cake mixes, oatmeal, etc. The moth lays eggs that hatch into caterpillars. The caterpillars pupate into moths and that is likely what you are seeing. You should go through every box of food in your cupboards, closets, pantry and look for webbing and caterpillars. Typically you will find one or more items infected and these can be bagged up and tossed in the trash. Here is a fact sheet on pantry pests. You can call the Center at<personal data hidden> for more information or suggestions. 
https://homegarden.cahnr.uconn.edu/factsheets/pantry-pests-control-measures/