Water is stable
Liquid water is essential for life because it provides stability and richness. It is temperature-stable, with a high heat capacity (it doesn't get hot quickly when exposed to heat) that gives it a large heat of fusion (melts at a high temperature) and more importantly a large heat of vaporization (it takes a lot of heat before it steams). It is stable as a liquid, with a large liquid range; also, liquid water is denser than ice, causing ice to float and insulate large bodies of water so that they may remain liquid (otherwise ice would sink, killing everything in a pond or sea during a freezing winter).
This stability is due to water's excellent capacity for hydrogen bonding. Indeed, water contains only hydrogen bonding groups: a highly electronegative oxygen atom with two lone pairs and two attached hydrogen atoms (unlike methanol or ethanol), giving it two hydrogen bond donors and two hydrogen bond acceptors (more than ammonia). Liquid water has ~85% of all possible hydrogen bonds formed, and they are constantly fluctuating (ice has 100% and they are rigid). These hydrogen bonds make water very cohesive. (Also, ike all molecules, water is stabilized by Van der Waals interactions.)
Water is a good solvent
Water has a richness in its chemistry and capacity to dissolve compounds. It is amphoteric, allowing it to interact with biomolecules as either an acid or a base. Also, it can dissolve polar and ionic molecules, making it a good solvent. Water has a high dielectric constant of approximately 80, which is a measure of how well a solvent reduces the interactions between ions in a solution. Water forms electrostatic or H-bonding interactions with ionic and polar groups, but is repulsed by polar molecules.
The repulsion between water and nonpolar groups results in the hydrophobic effect, whereby there is repulsion between water (which is polar) and nonpolar molecules. A classic example of the hydrophobic effect is to try mixing oil and water. The polar water and nonpolar oil never really mix. Oil droplets can be shaken into tinier bits, but they coalesce back together afterward in order to minimize the surface area between the polar solvent and nonpolar solute. The more small droplets there are, the more surface area there is.
This is unfavorable because of a peculiar property: water molecules become ordered as they interact with the nonpolar solute. However, the universe tends toward disorder, towards entropy, and thus there is a minimization of surface area beween the solvent and solute. This is visible when oil and water separate into two distinct layers. Another example of the hydrophobic effect involves peptides. Nonpolar (hydrophobic) amino acid residues tend to be inside the protein structure, sequestered from the aqueous environment.
Hydrolysis is prevalent in nearly every biochemical process. ATP hydrolysis provides cells the energy they need. Proteins and polysaccharides are hydrolyzed into component amino acids and sugars. Also, water adds to alkenes to form alcohols, as in the fumarase reaction of the citric acid cycle.