Clutch drag happens when the plates fail to completely release. A dragging clutch will make it difficult to change gears, and if it's bad enough, may allow the bike to creep forward when in gear. Drag occurs when there's too much free play in the clutch release mechanism or when a mechanical problem prevents the clutch plates from fully separating. Outside of the obvious things, like an improperly adjusted clutch or broken release mechanism, drag is often caused by wear to the clutch hub and basket. If the fingers or splines develop grooves or notches, the plates may hang up or twist in them and fail to fully release when the clutch is disengaged. Overheating the clutch can also swell the plates and cause drag, though everything should work normally once things cool off.
I should mention that, by nature, wet clutches suffer from something called viscous drag, particularly when they're cold. Viscous drag occurs when the viscosity of the cold oil creates enough drag between the plates to transfer some torque, even though you're holding the clutch in. If the drag is severe, punching the bike into gear can result in a loud clunk and maybe a small leap forward, or even a stall. Normally, this is only a problem when the bike is started for the first time on a cold day, or too heavy an oil is used, but the solution here is simple. Just let the bike warm up for a minute, preferably with the clutch disengaged, during the first start of the day, before putting it in gear.