If Paradox is the backlash of the universe twisting to change the mage as the mage changes reality, then Resonance is the constant subtle current that surrounds the mage as an agent of change.
All mages (as well as sorcerers and psychics) have some form of common Resonance. While most only have a little, a single point in a single type, as they grow in power, their aura grows to cloak them, affecting their every magical working and their everyday mundane life as well.
Every mage's resonance is unique, in a way, and those trained to recognize it may be able to tell the difference between the magical workings of different mages, sorcerers, and psychics. More vulgar, flashy workings will show more of the signs of a mage's resonance than coincidental, subtle workings, but every rote and spell contains some level of it.
There are three main types of Resonance, corresponding to the triatic influence of forces and energy in the tellurian. Dynamic covers things in motion, change, chaos, creation, life, flashiness, and creativity. Static covers definition, construction, stability, sanity, and stasis. Entropic covers death, decay, enervation, and primordial nature.
The most obvious effect, as noted, is that resonance tends to color a mage's magic. A Holy Stroke cast by a mage with a Dynamic (Bright) resonance might radiate an unnatural light, whereas one cast by a mage with Entropic (Hidden) may seem semi-corporeal until it hits you. Generally, only the most appropriate resonance will affect a given effect or spell, as it would be difficult to describe the various changes from a spell cast by a mage with a large number of conflicting resonances.
Mechanically, resonance can make magic harder or easier. Generally, when casting any effect, if you have a resonance type that's appropriate to the casting, you gain a -1 difficulty break, but if you have a resonance type that opposes it, you take a +1 difficulty. If you have both supporting and conflicting, the higher rating wins. On a tie, there's simply no difficulty change. For instance, a mage with Dynamic (Colorful) 2, and Entropic (Hidden) 1 that tries to change a brick wall to a neon blue color will get the -1 difficulty break, but if they tried to fade the blue back to an unnoticeable gray, they'd take a +1 difficulty penalty.
In day to day life, resonance can make things difficult for mages dealing with normal people. While Sleepers can't inherently detect or see auras, they can feel on a certain level that mages carry that air of 'oddness'. Because of this, a mage may take a difficulty penalty equal to their highest appropriate Resonance trait when interacting with someone. This only applies if appropriate; Entropic (Shadowy) won't affect Intimidation rolls, but Static (Relaxing) might, so only use the highest one that specifically applies.
Perception + Awareness (Difficulty 10 - highest trait) can sometimes detect the idle presence of heavy Resonance, but it won't usually gather specifics; Mind 1 or Prime 1, however, can both detect the specific nature of it, as can Mana Manipulation at 1 or 2. When confronted with an active magical effect, this becomes a bit more detailed; Perception + Awareness, difficulty of (10 - highest Resonance) can detect specific Resonance types without magic.
Mind 2 can cloak a mage's own personal resonance (or that of another), as well, preventing it from manifesting in magic or affecting social rolls, and it can also be used to imprint the mage's resonance on something else temporarily. Mind 2 Prime 2 can be used to actually change or imprint resonances that the mage doesn't have direct access to.
A final note, mages themselves aren't the only things that contain resonance. Any sort of tass does, as does any node (This includes Dross, Treasures, Fetishes, Talens, Freeholds, and Caerns, too). When using the quintessence from such a source, you need to take into account that resonance as well. Other supernaturals have it too, but they're affected by it in their own ways and have their own rules.
Resonance is very difficult to lose, and generally involves permanent magic (which has its own issues) or gaining a directly opposing (Fully opposite) resonance type to cancel it out.
Gaining it, however, while not easy, is doable in a multitude of possible ways:
A Seeking will just about always give a Mage a point of resonance, whether they succeed or fail.
An Outstanding or Impossible level effect may cause a mage to gain resonance if it succeeds or botches. (Ask an ST)
Falling into Quiet may gain you a point of the appropriate type (Dynamic for Madness, for instance).
Resonance may simply develop over time to match with a mage's use of magic, at ST discretion.
Below are a handful of different descriptors that might apply to each of the three types of Resonance. Feel free to come up with your own, this is just something to start with.
Dynamic: Quick, Flashy, Unique, Creative, Spinning, Whirling, Frantic, Frenzied, Intriguing, Liberating, Novel, Colorful, Bright, Flashy, Scrambled.
Entropic: Seething, Bubbling, Destructive, Corrupting, Withering, Disintegrating, Chaotic, Subtle, Primal, Ravaging, Fiery, Dark, Shadowy, Enervating.
Static: Protective, Sturdy, Single-Minded, Focused, Intense, Patterned, Tiered, Enfolding, Encompassing, Defined, Programmed or Illuminating. oh and ťōḱěń R s 1