Oil will suspend swarf, so it can be easily wiped away in use and replenished with some clean oil. Water won't suspend the swarf, so it'll settle much more quickly into the surface pores of the stone as you work.
The above isn't to say water can't be used at all. But in the longer term, the stones will be much easier to keep in good working order if they're used with oil. If used with water, more frequent cleaning & scrubbing will be needed to keep the stones from clogging and slowing down.
Even in cases where some swarf does settle into the pores of the stone when used with oil, it's much easier to 'float' or re-suspend that swarf by rubbing some clean oil on the surface with your fingertip. You'll see the oil 'dirty up' with the swarf picked up. Then just wipe it away with a rag (a microfiber towel works very good for this). This technique won't work nearly as well (or at all, really) if trying it with water alone. That's why the long-term maintenance is so much easier if the stones are used exclusively with oil.
