When you sharpen your knives with a sharpening stone, metal filings fly off of the blade. Combined with grit and grime, these filing can dirty the stone and reduce its efficacy.
Cleaning your stone can prevent this buildup from hindering your knives. If your sharpening stone is only lightly dirtied, a quick rinse with soap and water will suffice.
However, if your stone has significant buildup, apply a lubricant such as honing oil or WD-40, then use a scouring brush to remove the grime. Afterward, rinse it with warm water.
Allow the stone to dry before using it again. Arkansas stones and natural stones need special treatment: Submerge them in boiling water to release the buildup, then scrub it away.