Typically because it has more surface area than the typical air cooler. Many people who roll their own liquid cooling setups use 2x120mm radiators or even larger.
That's exactly what it does. Those parts are called "heat exchangers." CPU block lets the CPU heat up the liquid thus being cooled. Radiator lets the liquid heat up the air passing through it, thus the liquid being cooled.
Liquid cooling - cooling with liquid (which can be water)
Water cooling - cooling with water only
Since it doesn't get below 0°C, antifreeze isn't needed. What IS needed are two things. One is a corrosion inhibitor, which you can avoid needing by having every piece of metal which touches the liquid be either the same (basically don't mix aluminum with copper), or something that doesn't corrode. The other is an antimicrobial agent so stuff doesn't live in the liquid. Silver actually works as such. Thus, you can have real "water" cooling with something silver in the loop and everything else being (typically) all copper, or plated.
