In Ægir's hall there is no fire. Gold is laid on the floor and it gives light like flame, and the ale serves itself: the cups fill by themselves and there are no servants.
That detail — from the prose introduction to Lokasenna and from Skáldskaparmál — is the origin of one of the most-used formulas in skaldic poetry. Gold is eldr Ægis, Ægir's fire, or the fire of the sea, or the light of the water. Every time a poet reached for that image he was invoking a specific room.
Not quite a god, not quite a giant
The sources never classify him. He drinks with the Æsir and hosts them; Snorri also calls him a giant, and Skáldskaparmál opens by describing him as a man skilled in magic who travelled to Ásgarðr and was received as a guest, then repaid the visit.
His alternative names are Hlér — preserved in the Danish island name Læsø, from Hlésey, Hlér's island — and Gymir, which is also the name of Gerðr's giant father, producing a collision the sources never resolve. His genealogy in Skáldskaparmál's prologue material makes him a son of Fornjótr along with the wind and the fire, a triad of elemental brothers who look more like a learned Icelandic scheme than an inherited myth.
The most honest answer is that Ægir is the sea itself, addressed as a host. The word ægir is a common noun for ocean in Old Norse poetry and survives that way; whether the personification came first is unanswerable.
The cauldron
Hymiskviða exists because the gods want to drink at his hall and he does not have a vessel big enough. He says he will brew ale for them all if they can bring him a cauldron large enough — knowing, the poem implies, that there is not one.
Týr knows where one is: his father Hymir has a kettle a rost deep, a league or more. He and Thor go and get it, which involves the fishing expedition, a smashed drinking-cup, a pursuit by a many-headed host of giants, and Thor carrying the cauldron home on his head with the handles round his ankles.
So the whole plot of the poem, the famous fishing episode included, is a catering problem. The gods needed a big enough pot for a party.
Lokasenna happens here
The feast the cauldron makes possible is the setting for the most destructive poem in the Edda. Ægir holds the ale-feast; the gods attend; peace is declared over the hall, meaning weapons are set aside and no violence may occur. Loki kills a servant, Fimafeng, at the door, is driven out, and comes back to invoke an old right of hospitality — he and Odin were blood-brothers, and Odin once swore never to drink unless ale was brought to them both.
He is given a seat. Then he insults every deity present in turn, each accusation tailored, and the peace of the hall means nobody can touch him. It takes Thor's arrival and four repeated threats of the hammer to get him out.
Ægir's role in his own poem is to be the host who cannot eject a guest. See Loki's flyting for the full sequence.
The brewing
Skáldskaparmál names two servants who survive: Eldir and Fimafeng — the latter until Loki kills him. Ægir's association with brewing is strong enough that skalds use his name in kennings for ale, and the mythological brewer of the gods' drink being the sea is a satisfying piece of northern logic. Salt water is what surrounds the world; ale is what makes a hall a hall.
His wife, and his daughters
He is married to Rán, who catches drowning men in a net, and they have nine daughters whose names are all descriptions of waves: Himinglæva, Dúfa, Blóðughadda, Hefring, Uðr, Hrönn, Bylgja, Bára and Kólga in the usual list, though the names vary between sources. Bloody-haired, billow, the towering one, the cool one.
The nine daughters have been proposed as the nine mothers of Heimdall, which would make the watchman of the gods a son of the waves. It is a guess with no textual support beyond the number.
The household is the corpus's most complete family of sea-powers, and it divides the sea's meanings neatly: the husband is the sea as a place of hospitality and wealth, the wife is the sea as a taker of lives, and the children are the individual waves. See dragons and serpents for the other thing living out there, and the Norse overview for the tradition.
The name that outlived the god
The name is thoroughly alive: Ægir is a common Icelandic given name, an Icelandic coast guard vessel, a Norwegian brewery, and — most fittingly — the standard Scandinavian word for the sea in poetic register. The tidal bore on the River Severn in England is called the Severn Bore, but the equivalent phenomenon on the River Trent is the Aegir, a name usually derived from him and one of the few pieces of Norse mythological vocabulary still attached to a natural event in Britain.
Do the Æsir worship or fear Ægir?
Neither. The relationship in the sources is reciprocal hospitality between equals — he visits them, they visit him, and both parties are expected to provide a feast. That is a social arrangement between households, not a hierarchy, and it is the clearest example in the corpus of the gods dealing with a power outside their own group as a peer. It also means the sea in Norse thought is not something to be propitiated so much as someone whose invitations you accept and whose brewing standards you respect.
Are Ægir and Gymir the same person?
Snorri says Ægir is also called Gymir, and Lokasenna's prose calls the hall Gymir's. But Skírnismál makes Gymir the father of Gerðr and a giant of the mountains rather than the sea, and Gerðr is never called Ægir's daughter. Either two figures share a name, or one figure has two incompatible sets of relations attached to him. The name may derive from a word meaning "earth-dweller" or "the concealer," neither of which resolves it.