It is not an English word. It is usually a surname (I am not sure of which language). I have linked the Wikipedia entry for Ledbetter at the bottom of this post, and it does not have a meaning outside of surnames or names of towns (which probably came from a surname).
Ledbetter - Wikipedia, the free encyclopedia
EDIT: This was on the "Yellow Ledbetter" Wikipedia entry:
"The song title "Yellow Ledbetter" is derived from the actual name of an old friend of Vedder from Chicago, named Tim Ledbetter." So it is from a surname, and not an actual thing.