"Someone in despair despairs over something. So, for a moment, it seems, but only for a moment. That same instant the true despair shows itself, or despair in its true guise. In despairing over something he was really despairing over himself (...)"
-Søren Kierkegaard, "The Sickness unto Death"
Whereas humans are ambivalent creatures whose natures are insufficiently cohesive to allow such distortions or fractures, celestials for all their power are nonetheless internally rather delicate. Certain actions, physical or psychological, can create notes of dissonance that impair their natural abilities and open the possibility of Falling (for most angels) or Discord (for either angels or demons).
As the Game Master's Guide explains rather well, dissonance is not a series of "invisible tripwires" laid out as traps for celestials. Rather, being dissonant means choosing willfully to go against one's basic nature. It's deeply traumatic and rather painful. But sometimes, in a vaguely self-destructive sort of way, it feels better than the alternative.
There are several ways of healing dissonance. (These are mostly house rules.)
Sometimes, it's possible to make it all right on one's own. This requires reversing the outward expression of dissonance, which is not always possible: e.g., Impudites can't bring a dead person back to life. But if they do manage to reverse the outward expression, then, in close spatial and temporal proximity to the mending event, they can burn the dissonance away with 7 Essence. This requires a Will roll (for demons) or a Perception roll (for angels); the Essence is used either way. (Additional Essence can be used to raise the TN on this roll.) Failure means they wimped out or lost control, botching the process. If they have the Essence (perhaps from a reliquary), they can immediately retry after a failure.
Additionally, some resonances that can generate dissonance also provide a mechanism for healing that dissonance. This does not require any extra Essence.
Instead of using personal Essence to repair the dissonance, a celestial can also use a constant exposure to the ambient energies of a Tether. This takes one week, during which they absolutely cannot leave the Tether's grounds. (In the case of the Green Gecko building, it's the walls of the facility and a little bit of the entrance area.) Generally, the Seneschal will assign some task to them in the meantime, from guard duty to mopping the floors. At the end of the week, they can burn off the dissonance with 5 Essence.
This is not always a sure thing, and may require favors from the Seneschal, especially for demons.
Three notes of dissonance can be hardened into a single psychic scar -- a level of Discord -- at a cost of 3 Essence. They cannot choose consciously what type of Discord this will be, but the nature of their dissonance usually has an influence. This requires a Will roll (from both demons and angels), and the Essence is still spent on a failure.
A Superior can help a Servitor to heal dissonance, but generally speaking this is a rather rude (sometimes dangerous!) imposition. Even the nicest Archangels are apt to tell the Servitor that they need to deal with it themselves. And Demon Princes, well...