Hydrogen bond

An especially strong type of Van der Waals bond (with bond energy of 0.1 eV but the observed seperation between atoms with H-bond is smaller than it would be with only VdW bond).
Neutral hydrogen has only one electron - so it is expected to form a covalent bond with only one other atom. However, when bonded with the most electronegative atoms (F, O, N), the electron of the H-atom is alomost lost to the other atom. The bare proton of the H atomic nucleus can then form a bond with another electronegative atom - the bond being largely ionic in character. The atoms adjacent to the proton are so close that more than two of them would get in each other's way - thus the H-bond connects only 2 atoms.
H-bonds are much weaker than (say) covalent bonds - but when a large number of H-bonds act in unison, they make a strong contributory effect. The H-bond is an important part of the interaction between water molecules and is responsible for many of the striking physical properties of water and ice (including the hydrophobic effect and the unusually high melting & boliling points of water).

Water molecules are exceptionally prone to form H-bonds because the four pairs of electrons around the Oxygen atom in H₂O are not symmetrically distributed but are more likely to be found in certian regions of high probability density - arranged along the vertices of a tetrahedron. H atoms are at two of these vertices (which exhibit localised positive charges while the other two vertices exhibit more diffuse negative charges).
Each H₂O molecule forms H-bond with four other H₂O molecules. In the liquid state, these bonds between adjacent molecules are being constantly broken and re-formed owing to thermal motion. Even so, at any instant, the molecules are combined in definite clusters. In the solid state, these clusters are large and stable and constitute ice crystals. The tetrahedral arrangement of the four H-bonds that each H₂O molecule can participate in results in the characteristic hexagonal patterns of an ice crystal.
Structure of Ice
The hexagonal planar structure is responsible for the faceting planes and six-fold rotation symmetry of snowflakes.
With only four nearest neighbours around each molecule (instead of 12 as in closest packing) ice crystals have extremely open structures. This is responsible for the exceptional low density of ice [usually solids are denser than the corresponding liquid - but ice is less dense than water, which is why ice floats in water]. Because the molecular clusters are smaller and less stable in the liquid state, water molecules are, on the average, packed more closely together than are ice molecules. The density of water increases from 0 ^oC  to a maximum at 4 ^oC as large clusters of water molecules are broken up into smaller ones that occupy less space in the aggregate (only beyond 4^oC, the normal thermal expansion of a liquid manifests itself in a decreasing density with increasing temperature).

Introduction to biological macromolecules

Hydrogen bond plays a very important role in biology. A few of the multiple roles it plays are:

• holding the two strands of DNA double helix together,
• helping polypeptides (strings of amino acids) to form secondary structures (e.g., alpha-helix, beta-sheet),
• helping enzymes (bio-catalysts) bind to their substrate,
• helping antibodies bind to their antigen,
• helping transcription factors bind to DNA, etc etc.

Water molecules orient so as to form H-bonds even if the orientation restricts their mobility. So water molecules on the surface (i.e., an air-water interface) will have fewer water molecules with which to interact with than will molecules in the interior of the solution. The smaller number of possible bonding partners will mean that their possible orientations will be very limited in number - thereby lowering the entropy (compared to molecules in the interior). To increase entropy, water minimises its surface area. This is the reason for the high surface tension of water.

Non-polar molecules (e.g., hexane) which interact by VdW bonds and do not form H-bonds with water, also reduce the bonding possibilities of adjacent water molecules. Therefore, as in the case of air-water interface, the presence of non-polar molecules in water decreases the entropy of the system. Exclusion of these nonpolar substances from the aqueous solution will increase entropy. This entropy-driven effect where nonpolar molecules are grouped together and excluded from the solution, is known as hydrophobic effect - and non-polar molecules are known as hydrophobic substances. Correspondingly, polar molecules which can form H-bond with water are known as hydrophilic compounds. Note that nonpolar molecules do not attract each other; they are pushed together because they are mutually excluded from water.

For details on hydrophobicity, see the first few pages of Thermodynamics of Micelle Formation (Chapter 2, Fundamental Principles of Membrane Biophysics) by David Njus.

Hydrophobic effect is the fundamental principle for understanding biological membranes. Membranes give distinct identity to a biological cell. A cell is a ``chemical machine" to transform nutrients into building blocks for molecules with structural and functional roles, like proteins, DNA, polysaccharides, etc. Transport across the membrane is through active transport, which can occur even against a concentration gradient (in contrast to passive transport). Membrane is composed of amphiphilic molecules which are polar on one end and nonpolar on the other. By changing their concentration in water, several kinds of structures can be formed. In the cell, membranes are formed by phospholipids arranged in a  planar bilayer. Such a layer is impermeable to most substances - so to allow the passage of molecules into and out of the cell the membrane also has protein molecules embedded into it or attached to the surface (called integral membrane proteins and peripherial membrane proteins respectively). This is called the Fluid Mosaic model of membrane.
For further details on biological membranes, see the lecture notes on Fundamental Principles of Membrane Biophysics by David Njus.

The cell also needs a mechanism for storing information about how to build molecules (e.g., the sequences of amino acids needed to construct different proteins). This is stored in DNA.