St. Olaf's Day is in July, but reading the Saint Olaf's Saga has me thinking about customs associated with devotion to St. Olaf, including this hymn, which handily hits the major points in the hagiographical Life of Saint Olaf:
The title of Rex Perpetuus Norvegiae, King Forever of Norway, is first mentioned in the twelfth century, although the attribution seems to have been fairly widespread. Here is the explanation of it given in Saint Olaf's Saga in the Heimskringla, Chapter 18:
Thereupon King Óláf proceeded with his fleet west into Karlsá [Harbor], harried there and had a battle. Now when King Óláf lay in Karlsá [Harbor] waiting for a favorable breeze to sail to Norva Sound [the Strait of Gibraltar] and thence to Jerusalem, he dreamed a remarkable dream--that a man of commanding appearance, handsome but also terror-inspiring, approached him and spoke to him, bidding him give up his intention of proceeding further out into the world. "Return to your own possessions, because you shall be king of Norway forever." He understood this dream to mean that he would be king in the land, and his descendants kings after him for a long time.
[Snorri Sturluson, Heimskringla, Hollander, tr., University of Texas Press (Austin: 2018), p. 258.]
In reality, the only descendant of St. Olaf to be king of Norway was his illegitimate son, Magnus the Good. The kings of Norway since have generally been descended -- in one way or another -- from Harald Hardrada, Olaf's half-brother who tried to seize the throne from Magnus, but was forestalled by Magnus offering him co-regency; as it turns out, a very good deal for Harald, since Magnus died accidentally (and it seems to have been a genuine accident, not your usual royal-line-of-succession 'accident') the next year, leaving only an illegitimate daughter, Ragnhild. But St. Olaf has been the Eternal King of Norway ever since.
The lion-with-axe on the Coat of Arms of Norway (gules, a lion rampant or, crowned or, holding axe or with blade argent) represents St. Olaf as martyr and perpetual king.