The longer version
A split payment lets a doubles booking be paid in four parts instead of one. The organiser books the court, the other three receive a link, and each pays a quarter. Some systems hold the court until everyone has paid, others charge the organiser and refund shares as they come in.
Clubs are asked for it because the organiser is tired of chasing money. Players like it because nobody fronts the full price. The trade-off is complexity: partial payments, deadlines for the other players, and what happens when one never pays.
The common mistake is releasing the court when one player fails to pay, which punishes the three who did. Most clubs that offer splits charge the organiser for the full court and treat the split as a convenience for collecting, not a condition of the booking.