Disclaimer: The following is the outcome of a brainstorming with Patrick and Tom. Not all of the points apply to the magic in this world!
magic comes from crystals which have some sort of radiation that allows certain life forms to manipulate and "bend" matter
like FMA: matter can not just be created, only manipulated or transformed
magic casting is a little like programming
you have a goal in mind and multiple ways to achieve it
some ways are faster, but more dangerous, others slower but with a better result or better aim or whatever
weaving multi-purpose spell "algorithms" (like a generic framework) help casting spells
i.e. a fire algorithm that starts reactions with oxygen can be used to execute multiple fire-related spells
(more below)
a spell can have "bugs" and backfire if not properly "designed" or executed
i.e. healing spell to neutralise a poison can accidently melt the liver
to cast a spell, the caster has to activate certain areas in the brain (feels a little bit like following a chain of memories to a very specific memory that you could not access without going through these "helper" memories -> i.e. "where did I put my keys?" and then you start remembering the day from the beginning to arrive at the moment where you last had your keys)
every time a spellgorithm (hah, that's right! spell algorithm) is repeated, like neurons in the brain, connections between the spellgorithm-fragments get stronger, which means they can be accessed faster and require less concentration
i.e. if you cast a certain spell the same way thousand of times, you will eventually be able to execute it almost instantly and casually at any time (depends on the complexity of the spell ofc)
this makes new spells slow in execution and they will fail more often and "the good old spells" faster and "cheaper" in casting the more you use them
the crystal in the body of a magic user is complex and structured like a brain, so in order to fully understand and exploit your capabilities as a caster, you have to study the crystals and especially your own (much like programming, in order to fully use the potential of a code framework, you have to know what it's capable of and how it works behind the public API)
the color of a crystal shows the capabilities of it (it doesn't have only one color, most likely it is multi-colored inside)
imagine it like the GUI of a disk-cleaning tool for your harddrive, where you can see a box that is split in different sections, some for bigger files, some for smaller files and depending on the file type, they will be highlighted in a different color
a magic user can also use external crystals, but it is slower and possibly more complicated (like an external hard drive)
the "structure" of the external crystal is most likely unknown to someone who just picked up some crystal
if you find a crystal and carry it around some time and "get to know" it, you can use it to "store" spells on it, but when the crystal is not in reach, you cannot cast the spell on it
there is a common spell-language in the world -> wizards "copy" spells they know to external crystals coded in the "common" spell language that every wizard is taught, so it is easier to access the spell when someone takes it
a lot of crystals are sold that way, so the user does not have to learn the spell himself, but rather "use" the spell from an external crystal
you can ofc have crystals in your own "secret" language that cannot easily be read by others that try to use the crystal (but they can find out with enough time)
it is forbidden to sell crystals with some dangerous spells on it (there is probably some sort of blacklist for these spells)
they are sold anyways on the black market
some people have mutations -> no crystal or more than one crystal
your embedded crystal cannot run out of memory, but it may be that connections between structures can get smaller over time if you don't use them that often because you have this cool new spell that is so much better than the one before
like the human brain -> you will eventually forget things from your past if you stop thinking about them from time to time (because the connection of the synapses get weaker)
then it is helpful to engrave the spell to an external crystal, which only purpose is to contain this spell
(there is "space" for more than one spell on an external crystal)
some people collect or hoard crystals
if you have your embedded crystal in your arm and someone cuts off your arm, you cannot use magic anymore, sry
you can rip out your embedded crystal and sell it (or someone steals it), but the other person cannot instantly use it because the structure has to be "decoded"
structures in crystals "decay" after not being used for a long time (~100years)
crystals have a certain amount of stored radiation
casting a spell releases a portion of the radiation
casting too many spells in a short time will use up all stored radiation (like mana in some games)
the radiation builds up again over time, but it takes some time (like mana-reg)
how much radiation is used for a spell depends on the complexity of the spell (how much you have to "think" when using the spell)
there is a cap of how much radiation a crystal can store, but the limit can be extended:
by merging another crystal with your embedded crystal (pressing them together)
they must be compatible! like blood-type -> most crystals just don't merge, some people have a rarer crystal type and find almost no compatible other crystal :(
the merged crystal will be consumed by the embedded (it will not grow or anything, but you will know that it worked) -> the cap will most likely be extended by only a fragment of what the original crystal was capable of (imagine your embedded crystal has 1000rad, the external has 600rad, when merging, your crystal will only consume ~50rad of the external, leaving you with 1050rad)
experience
using a lot of spells, experimenting with spellgorithms, trying to develop a new spell, ... -> every time you had a breakthrough, your limit increases, too (ever had this moment while showering where you solved a mystery that was in your head a long time or though of sth. genius? moments like that!)