It is immensely stable as a liquid, compared to its chemical analogues. It has powerful solvent properties, and it has a very unusual behaviour with pressure. We all know that ice floats and we forget that this is very unusual behaviour. For moderate pressures and low temperatures the volatiles exist as solids. At moderate pressures and higher temperatures, each volatile exists as a liquid.
Liquid water is ubiquitous on Earth.
Liquid CO2 is unusual in our experience, although cylinders of pressurised CO2 for industrial use and fire extinguishers actually contain liquid CO2. The three lines on each phase diagram show the conditions where one phase changes to the other as pressure and temperature change. This change of phase may take some time to achieve, since energy must be either added to or lost from the system before the new form stabilises. Water in particular takes a lot of energy to change phase. There is a point where the three lines meet.