On a liquidity event, this lets preferred shareholders take their liquidation preferences and convert their percentage to common to share in the proceeds.
Let's say a sole investor has invested $2MM for 30% of the company at a 1X liquidation preference, with participating preferred. Soon after the company gets acquired for $10MM.
The investor can take their liquidation preference of $2MM from the $10MM payout, leaving $8MM for everyone else. With participating preferred, they'll also then take 30% of the remaining $8MM, $2.4MM, for a total take of $4.4MM.