Why is the landing distance increased on grass runways?
The long and short of it is that wheels are designed for smooth tarmac. While grass increases friction on the wheels on takeoff (making the aircraft work harder to get up to speed), it also reduces the efficiency of the brakes, thus taking longer to slow down.

And to add to @GdD's point, grass retains moisture much better than tarmac, so in wet conditions it is considerably slippier (and will remain so for longer afterwards).