Plain English Meaning
Two parallel runways are used for landings at the same time, but the planes on the two runways are not allowed to be side by side. Controllers keep them spaced diagonally so each pair has a safe gap between them.
Full Definition
An instrument approach procedure in which aircraft are cleared to land on closely spaced parallel runways at the same time, with required staggered (diagonal) spacing between aircraft on adjacent final approach courses. ATC ensures a minimum diagonal separation between each aircraft pair, so the approaches are conducted together but the spacing on one final depends on the spacing on the other.
Context Anchor
Seen in instrument approach procedures and air traffic control operations at airports with parallel runways.
Derivation
"Dependent" comes from Latin dependere, meaning "to hang from" -- one thing relies on another. Here, the spacing of aircraft on one depends on the spacing of aircraft on the parallel runway. That dependency is what distinguishes this from independent approaches, where each final is worked separately.