Other forms: underlaid; underlaying; underlays
To underlay a thing is to give it a foundation or support by putting something sturdy under it. Underlay also means to be underneath.
Something that underlays something else provides a base for that thing, whether it's the foundation of a building, the paper backing of a decal, or the fundamental ideas of a theory. As a noun, underlay refers to the padding that's laid out under carpet and other kinds of flooring.