Water is important because it is a major component of cells, typically forming between 70 and 95% of their mass and it provides an environment for aquatic organisms. It's molecules have an imbalance of charge (dipolar) and this generates hydrogen bonding between them.
Water is an excellent solvent for ions and polar molecules (molecules with an uneven charge) because the water molecules are attracted to them, collect around them and separate them, so that they dissolve. The chemicals are then free to move around and react with other chemicals and most processes taking place in living organisms, happen like this in solution. Non-polar molecules like lipids do not dissolve in water and tend to be pushed together by it. This is important in hydrophobic interactions in protein structure and in membrane structure. Due to it's ability to dissolve so many molecules, water is an important transport medium in animals and plants.
Water molecules are attracted to one another by hydrogen bonds and this restricts the movement of the molecules. This means that a relatively large amount of energy is required to increase the temperature of water (it has a high specific heat capacity) and that large bodies of water are slow to change temperature e.g. lakes and oceans. Due to their high water content, the bodies of organisms are also slow to change temperature and this makes maintaining a stable body temperature easier.
Water also requires a relatively high amount of energy to become a gas and this can be used as an effective means of cooling the body by sweating and panting. Conversely, a relatively large amount of energy must be transferred away from water to make it freeze, which is important for organisms with a high body water content and for those living in water.
Water is unusual because it's solid form is less dense than it's liquid form. Below 4°c the density of water starts to decrease and so ice floats on water and insulates the water below it. This reduces the chances of large bodies of water completely freezing and increases the chances of life in water surviving. These changes in density of water with temperature are important in the oceans because they set up currents, which circulate nutrients.
Water molecules tend to stick together and this is exploited in the way that water moves in long unbroken columns through the xylem tissue of plants and is an important property in cells. The cohesion of water molecules generates a surface tension at the surface of water enabling small organisms e.g. pond skaters to exploit it as a habitat.