(covers information from several alternate timelines)
This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
A well was a location where drinking water could be collected.
The Novans had underground wells in the tunnel and cave network beneath the surface on Terra Nova. When several tunnels collapsed, the Novan Akary was trapped under a large trunk inside a well but rescued by Jamin and Jonathan Archer. (ENT: "Terra Nova")
The Akaali had wells in the streets of their city on the homeworld. Some smaller ones were hanging at the walls and larger ones made out of stone were prominently featured in the center of the street. In 2151, Captain Jonathan Archer and the apothecary Riaan hid behind a stone well during a shootout with the Malurians. (ENT: "Civilization")
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")
In 3189, when inquiring about Michael Burnham's relationship with Cleveland Booker, Philippa Georgiou asked her, "So, what does this cat-loving friend have that made you fall for him like a two-year old on the edge of a well?" (DIS: "Scavengers")