Peeled potatoes get slimy in cold water due to the release of starch from the potato cells. This starch then hydrates and forms a gel-like substance on the potato's surface.
When you peel potatoes, you damage the cells on the surface. These damaged cells release starch granules. When the peeled potatoes are submerged in cold water, the starch granules absorb the water and swell. This process, known as gelatinization (though it's happening at a low temperature), causes the starch to become a viscous, slimy layer on the potato's exterior. The longer the potatoes sit in the water, the more starch is released and the thicker and slimier the coating becomes. This is why it's often recommended to only soak potatoes for a short period or to change the water frequently. The type of potato also matters; starchier potatoes like Russets will release more starch than waxier varieties.
To minimize sliminess, rinse the peeled potatoes thoroughly under cold running water before soaking. This helps remove excess surface starch before it has a chance to gelatinize.