The longer version
A box league divides players into boxes of similar strength, usually 4 to 6 per box. Each player plays every other player in their box once during the round, typically 4 to 6 weeks. When the round ends, the top 1 or 2 move up a box and the bottom 1 or 2 move down.
Clubs run box leagues because they give each player several matches against close opponents without a fixed schedule. Players arrange their own court times, which fills off-peak hours, and the promotion and relegation keep the boxes balanced round after round.
The measure that matters is completion rate: the share of scheduled matches actually played. When a large share go unplayed the standings stop meaning much. Common mistakes are boxes that are too big, rounds that are too long, and no rule for unplayed matches.