How does D&D 5E Wizard's magic work, in Lore terms?

Question

Not asking about the mechanics, but about the "lore" for the purpose of eg novel or short story.

Before, memorisation was represented in the following, IMHO coherent way:

You prepare a spell and mark it in your own mind, and can "feel" it as an entity of its own. To cast it, you find it in your mind, visualise it and release it using trigger components/words/gestures. Each spell is its own thing: if you want to cast it more than once, you have to memorise several instances.

Now, I'm not sure of how it should work. If it was presented in any Forgotten Realms novel, I've missed it.

The mechanics say that you prepare ("memorise", kind of) several spells beforehand. But then you can decide to only cast one of those prepared spells (of the same level), a limited amount of times per spell level.

How can this be justified, for a novel for example?

Answer 1

In Forgotten Realms lore, manipulation of magic is done through the Weave. The 5e interpretation of this is shown on pg. 206 in the side bar "The Weave of Magic".

[Mortals] make use of a fabric of magic, a kind of interface between the will of a spellcaster and the stuff of raw magic. The spellcasters of the Forgotten Realms call it the Weave and recognize its essence as the goddess Mystra, but casters have varied ways of naming and visualizing this interface.

Whenever a magic effect is created, the threads of the Weave intertwine, twist, and fold to make the effect possible.

Under "Known and Prepared Spells" on pg. 201:

Before a spellcaster can use a spell, he or she must have the spell firmly fixed in mind, or must have access to the spell in a magic item. Members of a few classes, including bards and sorcerers, have a limited list of spells they know that are always fixed in mind. The same thing is true of many magic-using monsters. Other spellcasters, such as clerics and wizards undergo a process of preparing spells.

Spell Slots represent the physical and mental exhaustion created by casting these spells (PHB 201, "Spell Slots"), which is why you can only cast so many spells between rests with the exception of cantrips, described as easier spells that are second nature to a caster.

Wizards differ from other spellcasting classes in that they completely study the Weave in a very scientific way. As you stated in your question, Wizards prepare their spells by fixing a certain number of spells from their spellbook in their mind for use during the day. The number of which is determined by a mix of the Wizard's intelligence and their study in the class (PHB 114). Wizards have a very wide array of spells at their disposal because they are masters of documenting the arcane. Other classes learn spells through a higher being or by practicing the physical aspect. Wizards are the only class in this edition who keep vast physical research notes to allow them to recreate not only spells they have experimented with but spells found on scrolls or other tomes.

Answer 2

The wizard's magic system in D&D came from the ideas of Jack Vance and some of his stories from over fifty years ago. The way you describe it is related to the older versions of D&D. Our colleague here, @aramis, found a good explanation for this:

Pre-4E D&D's magic system, ignoring sorcerers, is best explained by a visualization of spells as "knots" of mana.

For wizards, these knots are made using the spellbook page as a form; the spell literally can't be shaped without its assistance. The shape of the knot determines its function. Further, a wizard can only hold a few at first, but as they improve in ability, they learn how to tie more of them to themselves, as well as channeling more mana daily. At "Casting," what's being done isn't actually casting, but triggering the mana-knot to unfold so as to have the effect. This is based upon Bill Willingham's explanation of magic in the Ironwood graphic novels.

In 5e DnD, the model based on a Vancian magic system has been modified in that the wizard still prepares spells from a spellbook, but could cast one of the prepared spells multiple times based on whether or not enough spell slots of the correct level remain. That wasn't the case in, for example, AD&D 1e where the wizard loaded the clip (so to speak) in his mind. As each spell was expended it was unavailable until another preparation session (reloaded). Gary Gygax credited the Dying Earth series for strongly influencing his ideas on magic users.

A good explanation of this can be found at this answer here on RPG.SE.

per @AceCalhoun

Vance's Wizards are Limited to Concurrent Spells, not Spells Per Day

This is a matter of "gameplay" vs. "realism." Vance's wizards have a limit on the number of spells available at one time, without easy access to replenish their spells. D&D wizards are limited to the more "gamey" spells per day, with ready access to their spell books.

Insofar as "in fiction" justification, in Vance's world magic was rare, powerful and dangerous. Within the stories this added to the tension and sense of danger.

In fiction in 5e, the basic principle keeps the wizard bound to his spell books (a residual Vancian concept/fiction), but how the wizard used the magic available in the Weave (the in-fiction source of magic) is arbitrarily chosen as different from how the other spell casting classes tap into the Weave. They are all still limited by spell slots.