Adding to @PhilipKendall's great answer, the paddle in volleyball basically has the same functions as the electronic substitution board used in football. But the main difference is the paddle is carried by a player to hand over to the substituted player while the board is used by the fourth official.
They are used for the same purpose, i.e., to easily notify the substituted player, referees, and other officials that include those who monitor rule violations.
The main reason the paddle is used is to help keep track of the record moresubstitutions more easily for everybody involved. As multiple substitutions are allowed in volleyball, unlike football, including that for a libero who can be substituted as many times as possible, monitoring the number of substitutes and who is substituted is extremely difficult not only for officials, but also for coaches and players. Also, there is one more exception that an injured player (except the libero) could be substituted by another player beyond the limits of Rule 15.6.
What is the significance of the paddle?
It makes lives of everybody involved in the game easier.