Specific heat capacity. Water has a specific heat capacity of 4.2 J, which means that it takes 4.2 joules of energy to heat 1 g of water by 1°C. This is unusually high and it means that water does not change temperature very easily. This minimises fluctuations in temperature inside cells, and it also means that sea temperature is remarkably constant.
Latent heat of vaporisation. Water requires a lot of energy to change state from a liquid into a gas, and this is made use of as a cooling mechanism in animals (sweating and panting) and plants (transpiration). As water evaporates it extracts heat from around it, cooling the organism.
Latent heat of fusion. Water also requires a lot of heat to change state from a solid to a liquid, and must loose a lot of heat to change state from a liquid to a solid. This means it is difficult to freeze water, so ice crystals are less likely to form inside cells.
Density. Water is unique in that the solid state (ice) is less dense that the liquid state, so ice floats on water. As the air temperature cools, bodies of water freeze from the surface, forming a layer of ice with liquid water underneath. This allows aquatic ecosystems to exist even in sub-zero temperatures.
Cohesion. Water molecules "stick together" due to their hydrogen bonds, so water has high cohesion. This explains why long columns of water can be sucked up tall trees by transpiration without breaking. It also explains surface tension, which allows small animals to walk on water.
Ionisation. When many salts dissolve in water they ionise into discrete positive and negative ions (e.g. NaCl Na+ + Cl-). Many important biological molecules are weak acids, which also ionise in solution (e.g. acetic acid acetate- + H+). The names of the acid and ionised forms (acetic acid and acetate in this example) are often used loosely and interchangeably, which can cause confusion. You will come across many examples of two names referring to the same substance, e.g.: phosphoric acid and phosphate, lactic acid and lactate, citric acid and citrate, pyruvic acid and pyruvate, aspartic acid and aspartate, etc. The ionised form is the one found in living cells.
pH. Water itself is partly ionised, so it is a source of protons (H+ ions), and indeed many biochemical reactions are sensitive to pH. Pure water cannot buffer changes in H+ concentration, so is not a buffer and can easily be any pH, but the cytoplasms and tissue fluids of living organisms are usually well buffered at about neutral pH (pH 7-8).