Every spell in D&D shares the same format, with an easily trackable list of common attributes. With such a well defined structure, a spell is kind of an entity on its own. It can be ported to other games with different spell casting systems without massive changes to its theme. You're also more encouraged to treat it like an artifact; I can find a spell in a dungeon, written on the wall or in another mage's spellbook, and take it for my own, very much like a physical item.
Name
Description
At Higher Levels
Level
Spell School
Range
Duration
Components
Verbal
Somatic
Material
text of a physical component
Casting Time
Classes who can take it
Spells can be used for both in and out of combat. All spells can be cast at any time, even those that are explicitly cast for the purpose of harming or damaging. A lot of the fun for me is finding unique and creative uses for my wizard's spells. When it comes to combat focused spells in a more social or exploration focused situation, it can be fun for a wizard to focus more on the after-effects of a spell than the mathematics of how much it can damage an opponent. Fireball hurts, but it also catches things on fire; Thunderwave hurts, but it also pushes things around. I like that I can use a spell to fight battles and solve problems.
I think there's room for improvement on many of D&D 5e's spells here, however. More effort could be made to ensure spells have more uses than simply dealing damage.
Spells are self-contained and unique. In general, spells don't overlap, or rather, they don't ever do the exact same thing as another spell; instead they represent a very specific effect. This is true even if overlap does exist for all but a one attribute; when fighting a Fire Elemental, it matters if you wizard has Fireball and not Lightning Bolt. This is great for the act of actually designing new spells: it's easy to pick out one distinctive magical effect to write, easier than to creating an entirely new system with special rules (or theme of magic if your magic is designed more softly, without many strict rules). This opens the opportunity for just a lot of spells being written, which is just nice in general as it gives wizards a lot of choice while also making the wizards of the world more diverse via a unique combination of spell choices.
This is especially helpful for players like me who find it difficult to find creative solutions to problems using more general character traits, like "strong" or "dexterous" where the player has to find ways to use that trait in a creative way; personally I like that spells tell me exactly what my wizard is capable of--I can cast a spell and can be very sure of its effects and how they might relate to the situation at hand.
Spellbooks
Adding spells to the spellbook strengthens the fantasy of a studied and learned wizard. Wizards being able to read and copy spells is a great representation of how a wizard's connection to magic comes from a strong understanding of its underlying mechanics. Opposed to other spell casters that feel magic, or are granted magic by a higher entity, wizards learn magic by research and academics. The act of copying spells can be an extension of that: reading, translating, and copying is the exact same act a wizard would have performed while they learned magic before they're met in the our story. It's the natural progression of their magical knowledge and power; just like any other trade, the longer you've been doing it and the more you know, the better you are.
Every wizard has their own arcane syntax, which lends itself perfectly to personalization of the spellbook. A lesser recognized detail in the lore of wizards is that each wizard's spellbook is personalized to be an extension of the wizard. The reason spells take time (and money) to copy from another source is that each wizard writes spells differently. Each spellbook will utilize different symbols, formula syntax, and visual language to convey to the wizard how to cast its spells; it's written in essentially the wizard's unique shorthand. So, when a wizard is confronted with a spell drafted by another wizard, they have to spend a lot of time decoding it before it can be fully understood, and only then can it be copied.
Taking it one step further, wizards need not be restricted to the a regularly bound book for their "spellbook". Write your spells on loose leaf paper, get them tattooed on your body, engrave them onto rings and bracelets, embroider them into your clothes, enchant them into objects that must be held, create a deck of cards with spells drawn on them, write them on one giant scroll. Wizards (and characters in general) should be unique, and this is another way to reinforce that.
Wizards
Wizards are a widely understood archetype in fiction. Say the word "wizard" to anyone and chances are good that they have at least some mental picture of what that is. Popular media has solidified the idea of wizards in the public consciousness with a number of identifiable traits. People don't have to do a lot of onboarding to understand what role a wizard will fill in a group; in a roleplaying context, this is good for new players to have an easier time situating themselves in the story, as well as being good for experienced players as it allows them to more easily subvert expectations with their wizard characters.
Pointy hat
Long beard
Old
Mysterious
Smart
Magic staff
Wizards live in a world where magic can be exploited. Wizards, especially the ones written as having mastered magic through study, imply a significant detail about the world: that magic is a system that can learned. This is special because it differentiates the story of the world from other stories where people have less agency when it comes to magic. I'm thinking of stories where only a select few get access to magic (i.e. they are born with access or they were chosen by some ephemeral force that grants access), or perhaps stories where magic is more something to be dealt with than harnessed (i.e. magical natural disasters, magic related to monsters and hauntings, magic that tied to the existence of otherworldly beings and planes). Wizards have to exist in a setting where they can use their intelligence to bend magic to their will.
Things I Just Generally Like
I like the imagery of a wizard pouring over a bunch of notes and reading through ancient grimoires to find forgotten lore and magic.
I like the imagery of a wizard invoking magical effects by reading from a spellbook full of magical symbols, pictures, and arcane languages.
I like holding a set of my wizard's spells in real life. I like spell cards and I like putting them all together into a little book that I can read from at the table. And I like getting the chance to pick new spells and going to consult the big book of spells to find the right one to arm my wizard with.
I like getting new spells being tied to the world. Finding a spellbook on a dead wizard means my wizard is going to get a bunch of new toys to play with; I get those new spells without even needing to level up, and it means those spells came from the story and not an arbitrary meta resource like character level.
I like the idea that the spells a wizard has represents something about the kind of person they are, or the challenges they've had to overcome. My librarian wizard tries to pick spells related to understanding, reading, and learning; my hermit wizard, on the other hand, would pick spells related to making shelter, conjuring resources, hiding.
