Wikipedia
Walkdown
In country music, walkdown is a bassline which connects two chords whose roots are a third apart, often featuring an inverted chord. See: slash chord. A walkup would be the converse.
For example G and Em (a minor third apart) may be joined by an intervening chord to create stepwise motion in the bass: G-D/F-Em (I-V6/4-vi).
In jazz, a walkdown is a descending bassline below chords sharing a common tone. For example, if the above was G-D/F-Em7 the bassline would descend, G, F, E, while D is held in common.
Walkdown may also refer to the movement from V to IV in bars nine and ten of the twelve-bar blues.