According to pothole.info, the holes in roads were named in analogy to "pot-holes" where a river or stream has cut a similar hole in the bed, about the size and shape of a cooking pot.

According to Etymonline,

pothole (n.) 1826, originally a geological feature in glaciers and gravel beds, from Middle English pot "a deep hole for a mine, or from peat-digging" (late 14c.), now generally obsolete, but preserved in Scotland and northern England dialect… Applied to a hole in a road from 1909.

Oxford suggests that the M.E. pot meaning "pit" may be of Scandinavian origin.

The French nid-de-poule (hen’s nest) is much more colorful.

According to the OED, the origin of pot in this sense is uncertain. It may be from the Old Swedish potter, meaning 'a hole, well or abyss'.

pothole

/ˈpɒthəʊl/

noun
noun: pothole; plural noun: potholes

early 19th century: from Middle English pot ‘pit’ (perhaps of Scandinavian origin) + hole.
- Google.com