Each Muse has one Ideal that they subscribe to - it shapes their core beliefs and what sort of person they are. But beyond that, it dictates what influence they have over the Dreamscape. Their Ideals are their powers, and if they want to make changes to the Vignettes or the Dreamscape itself then this is the way to do it.
Each Ideal is a spectrum between two extremes, which gives each Muse wide-ranging powers over anything that falls between them - though as Muses age they will likely find they will tend to prefer particular balance. These extremes aren't necessarily good or bad - just two sides of the same coin.
At Character Creation, you must select one Ideal that your character is aligned to. These are:
These don't affect what faction your character may be a member of, though you might find one Ideal more useful than another if you're trying to do something specialised.
Once you've picked an Ideal, you'll have 4 points to invest in each your Skills. Each Ideal contains four Skills, which are the same across all Ideals, though the same Skill might manifest in a very different way depending on which Ideal is behind it.
More information on the Skills can be found here.