Does the purpose of the Schools of Magic mainly have to do with Wizard "Arcane Traditions" subclass options?  I know that for Aberrant Mind and Clockwork Sorcerers, that the list of spells that you can swap out the default spells you get with your subclass is partially defined by Schools of Magic and I think there might be some feats and perhaps other things that sort of work in a similar way to that  too. And I guess all the names of the schools have meanings and form categories that pertain to what various spells do or how they do it.  (maybe that helps to define what is possible to do with spells and magic)

It seems like spell cards usually include the Schools of Magic even though there's not much room on the cards, that always made me wonder if there was even more significance to Schools of Magic, something that I was missing. (I only recently made the connection with the Arcane Traditions and the greater purpose of having Schools of Magic is something that I've been wondering about for while.)  It kind of feels like if you aren't playing a Wizard whose subclass is defined by a School of Magic, or one of those  Sorcerers, that removing the concept of the Schools of Magic, wouldn't really change anything for you.  I guess Schools of Magic could add to the fun, I mean this is a game, it's supposed to be fun,  but I've not  really worked out a way to make the schools of magic add to the fun.    I think I might still be missing something:  could you please tell me what it is?

The school of magic exist for wizards but also to categorize spells despite having no rules of their own, some rules refer to them.

The School of Magic:  Academies of magic group spells into eight categories called schools of magic. Scholars, particularly wizards, apply these categories to all spells, believing that all magic functions in essentially the same way, whether it derives from rigorous study or is bestowed by a deity. The schools of magic help describe spells; they have no rules of their own, although some rules refer to the schools.

They were originally a purposeless* thing in 1e, or possibly earlier. Somebody decided that these were the divisions of magic, and all spells would fit into exactly one. They started getting mechanics attached in 2e.

They've always been an arbitrary set of classifications, and many spells fit poorly in the categories they're placed in.

IMO, it'd be much more useful to replace them with a general-purpose tagging system, but WotC don't ask me.

* As far as I remember. It's possible Illusionists got some kind of bonus with illusion spells, but I don't think so.

At one point it occurred to me that at least some of the names of the schools of magic, have an obvious verb form (divine, conjure, evoke, enchant, transmutate) and I thought that might be a sort of fun way to flavor spells, but I don't think that's true of all of them (or else I'm just uncomfortable with the verb form of "Necromancy").

Past edition also use to make it so if you specialized you could not take or use spells of of opposite school. This was also back when either you were a wizard or a specialist.

I thought the graphic from this reddit post was helpful what the names of the school mean and what the spells that belong to them do and then there was a "neat" acronym offered up for remembering all of the names of all the schools in one of the early posts:  https://www.reddit.com/r/DnD/comments/69f2kq/5eart_a_short_n_sweet_take_on_the_8_schools_of/?rdt=48578 

I'm getting the impression that the significance of the Schools of Magic is either pretty niche (mainly applies to wizard and certain sorcerer subclasses) or is a holdover from pervious editions. 

It's partly tradition, partly narrative, and partly because it allows for certain subclasses to show their specialization in certain magics by giving additional effects to certain spells.

So, the origin is a combination of Norton and Vance in the 73 to 76 time frame.

The primary purpose of the schools is to help guide the creation of new spells (mechanically) and to provide a way to categorize what kinds of spells certain creatures are immune to.

The original subclass of Illusionist was intended as a way to explain how illusions worked, as a grouping, and because it gave a bit more weight to the notion of schools. It is a taxonomy system, in the same way that we classify beings and end up with things like Homo sapiens sapiens.

They did indeed use the core magical verbs and traditional kinds of magic -- conjuring (summoning), transmutation (alchemy), invocation (uttering a spell), evocation (creation), necromancy (the dead), etc.

Over editions, these all changed somewhat as they expanded and contracted the spell list.

The biggest practical impact, mechanically, is found in the creatures that one can encounter. Some only use certain kinds of magic, others are immune to certain schools, and so forth. 

although the primary rules are unlikely to alter them much, many many games use entirely separate systems of classification for similar purposes, and to some extent the original concept of "domain" for clerics relied on that idea as well (though it no longer does.)

Quote from intrepidgnome >>

At one point it occurred to me that at least some of the names of the schools of magic, have an obvious verb form (divine, conjure, evoke, enchant, transmutate) and I thought that might be a sort of fun way to flavor spells, but I don't think that's true of all of them (or else I'm just uncomfortable with the verb form of "Necromancy").

 

 "I shall necromance you to death!"

Quote from RJP1973 >>

 "I shall necromance you to death!"

 yep, unconfortable

Quote from AEDorsay >>

So, the origin is a combination of Norton and Vance in the 73 to 76 time frame.

 

 I'm not familar with Norton and Vance; could you enlighten me? 

Quote from intrepidgnome >>

Quote from AEDorsay >>

So, the origin is a combination of Norton and Vance in the 73 to 76 time frame.

 

 I'm not familar with Norton and Vance; could you enlighten me? 

 
Jack Vance and Andre Norton? Authors (and early supporters of D&D) whose works had significant impact on the way magic works in D&D and on the game development?

Huh.

Both Gygax and Arneson were fans, and exchanged letters with them during the late development phase and the earliest years of TSR.  You can look them up via any of the assorted encyclopedias. 

Vance gave the core framework (spells do one thing, material components, fire and forget, and such) and then Norton had more influence on how to categorize stuff.