A wet clutch is immersed in lubricating fluid to keep the surfaces clean and to cool it, for improved performance and longer life; while a dry clutch is not. Since the surfaces of a wet clutch can be slippery (as with a motorcycle clutch bathed in engine oil), stacking multiple clutch disks can compensate for slippage.
Suzuki Web Site:
Lubrication: Semi-Dry Sump
From the Suzuki site: Suzuki Advanced Sump System - semi-dry-sump lubrication system featuring separate crankshaft and transmission oil chambers - permits low crankshaft placement for reduced engine height and low center-of-gravity (2005 RM-Z450)
Honda design on their GP bike:
According to Honda the RC-V's semi-dry-sump design, which puts oil in the gearbox cavity, also aids compactness as well as reducing blow-by. This cylinder angle gives perfect primary balance, so no power-sapping counterbalancer is needed.