Answer:
You are opening a huge can of worms asking this question.
Furries, in general, are people who feel some sort of attachment to an animal/animals.
They range from people who just really like animals to people who feel a spiritual connection to them.
There are those who like to dress up like animals, draw pictures of animals, give human characteristics to animals, feel that deep down they ARE an animal, etc.
The reason this question is so difficult to answer is because the furry spectrum is great. I suggest doing lots Googling to get an idea. Be careful, furry artwork can be a bit umm.. much.
(minor edit, took out inter-species relationships with animals. this is a common misconception spread by 4chan originally. do not get furry fandom confused with zoophilia. furries are against that)