According to Funn, this is her explanation of what a daemon (pronounced 'demon') is:

"...the concept comes from His Dark Materials. A daemon is the physical representation of your soul in the world which His Dark Materials is set in. It is always an animal and is almost always your opposite sex. This daemon will follow you throughout your life and when you die you daemon fades away. You can't seperate from your daemon and if you do, which is the very basis of how His Dark Materials started, you will be like a wondering being without a soul and that is not good. Your daemon can be a shape shifter when you're a child but when you're matured as in come off age your daemon will settle into one permanent form. Can be a monkey also or I suppose a rat. Depending on your personality. "

Hmmm... deep.