place
Hliðskjálf
Odin's high seat, from which he can see over all the worlds; Frigg shares it with him, and Freyr's one forbidden turn in it costs him his sword.
Hliðskjálf is Odin's seat of vision. When Allfather sits in it, Snorri says, "he looked out over the whole world and saw every man's acts, and knew all things which he saw" Gylfaginning 9. It is the place from which the gods notice things, and several stories begin there.
Who sits there
The prose frames of two Eddic poems open in Hliðskjálf. In Grímnismál, "Othin and Frigg sat in Hlithskjolf and looked over all the worlds", and from there they watch their two foster-sons and make the wager that sends Odin to King Geirröðr Grímnismál, prose 2. In Skírnismál, Freyr sits there one day, looks into Jötunheim, and sees Gerðr Skírnismál, prose 1. The poem passes no judgment. Snorri does: Freyr was punished for "having presumed to sit in that holy seat" by falling helplessly in love Gylfaginning 37. He bargains away his sword to win her (see Freyr and Gerðr).
Odin uses the seat in Snorri's account of Loki's capture: Loki hid in a mountain house with four doors, but "Odin had seen from Hlidskjálf where he was" Gylfaginning 50. A skaldic verse calls Odin "The Mighty One of Hlidskjálf" Skáldskaparmál 2.
Seat or hall?
Snorri is not consistent. In one chapter Hliðskjálf is "one abode" in Ásgard Gylfaginning 9; in another it is "the high-seat so called" inside Odin's hall Valaskjálf Gylfaginning 17. The Eddic prose says only that gods "sat in" it. Whether Frigg's and Freyr's use of it was normal or a liberty depends on which source one follows.
In the sources
Quoted from the hosted translations; each line is checked against the text when the site is built. Select a reference to read it in context.
There is one abode called Hlidskjálf, and when Allfather sat in the high-seat there, he looked out over the whole world and saw every man's acts, and knew all things which he saw.
Othin and Frigg sat in Hlithskjolf and looked over all the worlds.
Freyr, the son of Njorth, had sat one day in Hlithskjolf, and looked over all the worlds.
Thus his overweening pride, in having presumed to sit in that holy seat, was avenged upon him, that he went away full of sorrow.
and Odin had seen from Hlidskjálf where he was.