The phrase was coined by Ray Harryhausen who came up with the method at the beginning of his stop-motion career. It involves crafting a wire armature (instead of ball and socket) and then applying thin sheets of upholstery foam over it for muscles and then painting latex over it. Afterwards the puppet is given skin texture and is painted for a overall finish. The overall look of the puppet if done right is amazing.
Here are a couple of links for you to check out if you are interested in crafting your own build-up puppet:
The Lone Animator - an brilliant site crammed full with tons of images and vids of puppets made by using build-up.