This is a measure of your strength of will, your psychic power, your magical aptitude, and your spiritual power.  High psyche people draw others to them, even if they don't want to, and tend to dominate social situations, whether by charisma or by sheer force of personality.

Psyche is often used to determine how well your powers work and how much control you have over them.  It's also used in psychic combat, when minds struggle directly.  It can be intended to cause mental damage or alternately to invade people's minds, stealing their secrets or controlling them.  Psychic combat can be initiated by either touching your opponent, establishing eye contact, by magic, or by Trump contact. There are other means, but these are the most common.  (For example, in some shadows, you can communicate mind to mind with ease while in different cities or even continents)

High Psyche helps you to:

Approximate Levels of Psyche

Human (-25)

You have the willpower of an average human, which means that in the Amber scheme of things, you're feeble.  The average Amberite can crush you like a bug in psychic combat, and anyone above Amber rank can peel your mind like a grape in seconds.  You can't even initiate psychic combat.

Chaos (-10)

Your will is on a level with that of major world leaders on Earth.  You can initiate psychic combat.  This is the average rank in Chaos, while in Amber someone at this rank is considered somewhat weak willed.  Anyone with 1 or more points can still squish your mind like a grape, but it may take a little time if they don't have too many points.

Amber (0)

The best real world human who ever was, an above average Chaosian, or an an average Amberite.  You can initiate psychic combat, easily beating those of Human rank and defeating those of Chaos rank with effort.  Only those with 76 or more points of Psyche can beat you with a single psychic blow if you're ready for them.

Bottom Ranked (1-10)

Average Amberites specializing in Psyche will generally be found in this range of points.

Low Ranked (11-20)

People at this level are considered strong willed in Amber.

Middle Ranked (21-50)

This is the realm of the consumate professional.  Powerful sorcerors and powerful shapers of Shadow by means of Pattern or Logrus will generally fall into this range.

High Ranked (51-75)

This is a very exceptional level of psyche, possessed generally by only the best.

Best Ranked (76-125)

This is nigh-unbelievable strength of will.  People at this level can crush others psychically incredibly quickly.  Indeed, sometimes, you may mold others to your will without realizing it if their psyche is substantially lower than yours.Anyone with Amber psyche or lower is basically your puppet with no real chance of saving themselves.

Exalted Rank (126+)

You pimp-slap Fiona and Dworkin in your spare time, most likely.  You have a god-like will.  Anyone with ten or less points of Psyche will pretty much collapse in the face of your psychic might.