Several things happen when you add antifreeze to water:
Reducing the freezing point
Well, this is obvious. While pure water freezes at 0°C, ethylenglycol can put it down to -55°C for a 60:40 (6 parts antifreeze, 4 parts water) mixture. However, it's interesting that the freezing point goes up to -15°C again, if you add more antifreeze:
(Sorry for the german. x-axis: fraction of antifreeze in %. y-axis: freezing point)
Increasing the boiling point
This was already mentioned in the other answer. The 60:40 mixture increases the boiling point from 100°C to 115°C. This is not so much, but since 90°C is not an uncommon coolant temperature, this gives some extra safety margin. By the way, the cooling system is pressurized when hot, which increases the boiling point a little more.
(Sorry again for the german...)
Decreasing the heat capacity
Water has one of the highest heat capacities of 4.2K / (J * g), which means you need an energy of 4.2J to increase the temperature of 1g of water by 1K. Antifreeze has only about 2.4K / (J * g) , and when mixing both, you get about 3.4K / (J * g). This means, your engine will heat up to nominal temperature faster but also, the mixture can not carry away as much heat as pure water could. However, this is compensated by the higher boiling point of the mixture.
Preventing corrosion and more
Well, you already got the link to Running with straight water as coolant in the summer. Is it fine? . Antifreeze contains inhibitors which reduce limescale and corrosion in your engine.
Note: While distilled water will not cause limescale, it is more aggressive to metal than tap water, and causes more corrosion.
Another point is cavitation. At the water pump (and other places in the cooling system) local spots of strong under-pressure can exist in the liquid due to its fast flow. Small bubbles of vapor occur there, and collapse again when they leave the under-pressure region. When they collapse, they create strong shock waves, which can damage nearby materials. This is what destroys ship's propellers over time and may also damage your pump over time. Antifreeze can reduce the effect.
Long story short:
Reducing the freezing point is the most obvious, but not the only task of antifreeze in your engine. So, use it even when you're in a frostless region.