It's a bit more affectionate than "mate" and usually refers to someone younger than oneself. The youngest member of a family will often be called "our kid" by the rest of the family, and by the family's close friends.
coming from Manchester originally, we used the term "our kid" to all our sisters, also "our Mum" "our Dad", I was told that it relates to belonging to. Even used for other relatives, It seems to be used more in Liverpool though.