The poem opens with a wonder-struck exclamation: "What mystery pervades a well!" The following lines elaborate on that statement, which might strike the reader as counterintuitive: after all, what's so mysterious about an ordinary water well?
Modern home wells typically pump water directly into indoor plumbing systems, but Dickinson is describing the kind of old-fashioned well that was common in mid-1800s New England. Water is drawn from such wells by hand, usually via bucket and pulley. Anyone drawing from the well will be able to peer into its depths.
So the well might seem mysterious, first and foremost, because its depths are gloomy, remote, and hard to fathom. In fact, the speaker compares the "water" lurking "far" down in the well to "A neighbor from another world," occupying the deep "jar" of the well shaft. Notice that this metaphor contains elements of both personification and paradox. To the speaker, the water seems mysteriously alive, like an intriguing "neighbor." But whereas ordinary neighbors are defined by their nearness, familiarity, etc., this water seems distant and otherworldly. Upon reflection, this paradox makes a certain kind of sense, because the water in a home well is at once close (maybe even part of one's own backyard) and distant (so far beneath ground level as to be inaccessible).
If the well water seems to "Resid[e]" in a deeply buried "jar," the "lid" of that jar seems to be made of "glass"—meaning, of course, the glassy surface of the water. The speaker stresses that this surface is the only part of the water visible from ground level. Indeed, the speaker claims that "none have ever seen" the "limit," or bottom, of the well. (Depending on how the well was constructed and whether it ever dries up, this claim might be hyperbolic.) So the basic "mystery" that "pervades [the] well" is a visual one: what does the bottom look like? What's down there that we can't see? This visual obscurity, in turn, might symbolize other kinds of mysteries and "limit[s]," such as knowledge human beings can't access.
For some, peering down into that deep water might also be dizzying or frightening. After all, people have accidentally fallen into wells! Besides, any presence that we can't see or touch has the potential to unnerve us. So the well carries an element of danger as well as mystery—an element that will become more important as the poem goes on.