A child, generally of a young age (but not limited to) which is fitted with a harness with a leash attached to it. It is used so the parent then can control the movability of the child. Leash kids are seen in many shapes and sizes, ranging from little children that run a muck to fat ones that destroy things.
Little girl: "Look at that kid mum, his on a leash"
Mum: "Shhhh, stop staring at the leash kid"