Wikipedia does a good job of summarising the concept of a dæmon:
A dæmon (pronounced like “demon”, but is unrelated) is a manifestation of a person’s soul in the Philip Pullman trilogy His Dark Materials. In those universes with physical dæmons, they exist external to the human in the form of animals representative of the person’s personality, although children’s dæmons may change form at whim. The bond between dæmon and human is intimate, and dæmons must remain within a small distance of their human (with the exception of witches)…
It is similar to a number of traditional concepts of avatars and personal representation such as familiar animals or witchcraft poppets, and, for me, ties in closely with modern puppetry and personal robotics.
