Four-way close means playing all four chord tones in close position with one hand — typically the right hand. Each of the four inversions puts a different note on top, which is crucial for chord melody where the top note carries the melody line.
All four inversions of close position, each spanning 12 semitones or less. Root position, 1st inversion (3rd on top), 2nd inversion (5th on top), 3rd inversion (7th on top).
For chord melody playing where the melody note determines which inversion you use. The top note of a 4-way close voicing IS the melody. This is the George Shearing technique — pair it with melody doubling an octave below for the full locked hands sound.