small bucket; small pail
A small container used for carrying water or other liquids, often made of wood or plastic. Not a common everyday word; バケツ is more frequent for modern buckets.
In the old days, people drew water from the well with a small bucket.
Compound of 小 (small) and 桶 (bucket, tub). The reading こおけ is a straightforward combination of the kun'yomi readings.