Smooth motion between chord tones
Voice leading refers to how individual notes move from one chord to the next. In a progression from C major (C-E-G) to F major (F-A-C), the smoothest voice leading moves the C up to F (a fourth), the E up to A (a third), and the G down to C (a third). Each voice takes the shortest path to the next note, avoiding big jumps. This creates smooth, connected harmony that flows naturally.
When voices jump around chaotically, the chord progression sounds awkward and disjointed, even if the chords themselves are correct. Professional arrangers spend as much time on voice leading as they do on chord choice, because the quality of movement between notes is often what distinguishes polished arranging from competent but mechanical work.
Parallel fifths and standard rules
Parallel fifths (two voices moving in the same direction by the same interval) and parallel octaves violate classical voice-leading rules because they blur the distinction between voices. Modern music often breaks this rule intentionally (especially in rock and electronic music), but understanding the rule first makes intentional breaking more effective.
Contrary motion (two voices moving in opposite directions) is always smooth and preferred. Oblique motion (one voice stationary while another moves) also works well. These principles are not restrictions but shortcuts to voice leading that sounds naturally smooth. Jazz and classical composers follow them because the rules evolved from centuries of what actually sounds good to human ears.