There are actually two important Spanish holidays on this date; the Fiesta Nacional, chosen to commemorate Christopher Columbus’ landing in the Americas, and the feast day of Our Lady of the Pillar. The former might be more official, but the latter is apparently more popular culturally – understandable in a majority-Catholic country. She is the patron saint of the Civil Guard, and also of the region of Aragon, which provides a nice segue into discussing the Spanish national arms!
Blazon: Per quarterly, I gules a castle triple-towered or windowed argent (Castile), II argent a lion rampant purpre crowned or (León), III or four palets gules (Aragon), IV gules a chain in saltire, cross, and orle or, charged with a center point vert (Navarre); enté en point argent a pomegranate slipped, leaved, and seeded proper (Granada); overall in the fess point an escutcheon azure three fleurs-de-lis or within a bordure gules (Bourbon-Anjou)
Supporters: Two columns argent, capitals and bases or, standing on five waves azure and the first, the dexter surmounted by an imperial crown and the sinister the Spanish royal crown proper, and entwined with a ribbon gules charged with “Plus ultra” of the second
The current depiction of the arms was formally granted in 1981, but the individual elements are all very old. The first two quarters of Spain are the best counterargument I’ve ever seen against the idea that canting arms are somehow ‘lesser.’ (Canting arms are arms that are essentially puns on the name of the family, country, etc. – think mountains for Bergs, eels for Ellis, etc.) There’s a weird idea in some heraldic texts that canting arms are less “noble” than non-canting arms. But Spain features three coats of canting arms, beginning with the somewhat obvious Castile and León.
Castile and León were two of the more powerful states in medieval Spain. They went back and forth between unified and not for a few centuries until they were formally unified under Ferdinand III in 1230. The lion and castle show up in a lot of Spanish arms, usually as quarters or smaller sections, although often the lion will be rendered gules instead of purpre. (Gules is a much more common and easily-rendered tincture in heraldry than purpre.)
The third quarter, the widely-used Bars of Aragon (not bars in the heraldic sense), joined the arms along with the Crown of Aragon when Isabel I of Castile – the several-times-great-granddaughter of Ferdinand III – married Ferdinand II of Aragon in 1469. The pomegranate (the third canting element) was added shortly afterwards, perpetually enté en point, after the conquest of Granada was concluded in 1496 and it was added to the Spanish crown.
It is with immense gratitude that I can skip over the two hundred years of Habsburg rule in Spain, because while their arms are mind-bendingly complicated, none of the several dozen coats with which the Spanish arms were combined stuck around. However, the kings of Spain used the title “King of Navarre” after the War of the League of Cambrai, and some of the variants of the Spanish arms (especially those used in Navarre) incorporated the chain figure, especially as an escutcheon. A smaller version of Navarre officially survived as an independent kingdom until they were incorporated into Spain in 1833, which is also when the Navarre arms start showing up as a full quarter in the Spanish royal arms.
The last of the current elements of the Spanish arms appear when Philip V inherited the Spanish throne in 1700. Philip was a Bourbon – specifically, of the cadet line of the dukes of Anjou. Because everyone in European royal circles was pretty inbred at this point, his arms as the King of Spain also included Austria, Burgundy, and Flanders, among others. However, he bore the arms of Anjou in an escutcheon, and that’s stuck around since then. My theory is that they’ve also stayed in the escutcheon due to the agreement laid out in the Peace of Utrecht that the French and Spanish crowns would never be unified. Because of that, the Spanish monarchs could only “pretend” to the French throne, and never have any territorial claim.
Finally, while the unique supporters aren’t quite canting, I think they’re worth a mention. They are, specifically, the Pillars of Hercules, which flank the Strait of Gibraltar, i.e. Spain’s gateway to the Atlantic Ocean. The motto “Plus ultra,” or “Farther beyond,” is a reference to the legend that the pillars were carved with “Non plus ultra” to warn seafarers to stay on the side of the strait without (as many) storms and sea monsters and other such dangers. The removal of the negative is a nice nod to Spain’s history as a seafaring and exploratory nation.