Since water is a liquid, the thermal conductivity is not limiting the efficiency as coolant. Instead of relying on internal heat conduction away from the surface to be cooled into the water bulk, water is a fluid, thus the heat will be transferred by convection (natural flow due to temperature gradients) or forced flow of water by a pump, for example. If the water flow is strong enough, the limiting factor is the actual transfer of heat over the phase boundary between the solid to be cooled and the liquid.

Water is a actually a very good coolant because it has a very high specific heat capacity of 4.2 J/(K g). This is typically twice as large as organic solvents and at least 4-5 times, sometimes more than 10 times larger than most solids (relative to mass). Since the thermal energy or heat is conserved during the transfer, this means that water can reduce the temperature of the material to be cooled by a certain degree, while its own temperature is increasing only by a fraction of that (considering somewhat similar mass).

The very large heat capacity in combination with the ability to transport the warm water quickly away by forced flow makes water such a good coolant, which is furthermore easy to obtain and very cheap. One of its downsides is the relatively large corrosivity and its tendency to expand when (accidentally) freezing.

To expand a bit on the difference between heat conductivity and heat capacity: Metals are very good conductors of heat, but have poor heat capacity. This makes them feel cold, because they can quickly transport the heat away from your skin, but will also quickly warm up.