(covers information from several alternate timelines)
A well was a location where drinking water could be collected.
The settlement on Barkon IV where Gia and her father lived had a well in the town square. It was the closest source of fresh water for their village. In 2370, Data poured an antidote to the townsfolk's radiation sickness down the well, but they believed he was poisoning it instead. (TNG: "Thine Own Self")
In 2376, Edith Mulchaey recalled that her daughter Mary had fallen down a well once at Ballahick Farm, only to mysteriously be rescued before she could bring help. Initially, this lead to suspicion against "Katie O'Clare" and the other members of USS Voyager's crew who visited Fair Haven in the holodeck, but Michael Sullivan later used it as an example of their benevolent intentions. (VOY: "Spirit Folk")