A Noble Phantasm is a Servant's most powerful attack, its ultimate trump card.
The Servant's Noble Phantasm usually takes the form of some legendary artifact that the Heroic Spirit had when they were still alive.
For example, King Arther's Noble Phantasm would be Excalibur.
Not all Noble Phantasms are simple weapons.
For instance, it could be a shield, a mount, an army, or some supernatural ability.
Most Servants do their best to hide their Noble Phantasm for as long as possible, since keeping your Heroic Spirit identity a secret gives you a slight edge.
It is possible for a Servant to have no Noble Phantasm, but it is exceedingly rare.
Magic Circuit
Every Magus, without exception, has a magic circuit.
A magic circuit is like a second nervous system spreading through a magus's body, which connects the material world to the astral plane.
Using a magic circuit, a magus can channel the latent energy in their bodies to perform supernatural feats - in other words, magic.
One is born with their magic circuit, and it does not increase or decrease in strength naturally.
It can, on the other hand, be modified artificially.
However, doing so is very risky, as it can destabilize a magic circuit, rendering it unusable.
A stronger magic circuit makes for a stronger mage.
Magic circuits are hereditary - this is what causes magi to run in families.
Thaumaturgial Crest
In a lineage of magi, the most valuable and closely-guarded of treasures is the Thaumaturgical Crest.
A Crest is essentially an artificial Magic Circuit, branded onto the body of a magus's heir at an early age.
At some point during a magus's career, they expand and strengthen their Crest, storing power and spells inside it.
Then, when they have an heir, the Crest is transplanted to the new host, carrying with it the power of the previous magus.
This process continues, causing Crests to get more powerful the older a family of magi is.
Crests, like internal organs, can only be transferred to a compatible host - usually a blood relative.
It is perfectly possible to be a magus without a Crest, but it's much harder to be good at it.
Mage's Association
There is an international organization, founded by western magi, whose purpose is to control, devlop, and conceal Magic in the world.
This organization is called the Mage's Association.
The Association enforces many laws about what magi can and can't do without incurring their wrath.
Chief among these is the rule that magic must be kept secret from the public.
The Mage's Association knows about and monitors all major magus families, so only obscure or non-family magi escape their knowledge.
There are three branches of the Mage's Association.
The main branch is called Atlas, a.k.a. The Giant's Pit, and is located in Egypt.
Atlas governs over the other two branches, and is the most powerful of them all.
The second branch, Clock Tower, is housed in London.
Clock Tower runs a secret but very prestigious (among magi) school of magic, run mostly from the British Museum.
While it seems welcoming and friendly, Clock Tower is largely controlled by power struggles between rival factions of magi.
The last branch is Sea of Estray.
The Sea of Estray is a conglomeration of minor groups of magi spread all throughout Europe.
This is the oldest of thre three branches, most closely tied to the origins of magi in history.