Short answers, pulled from the story.
An intermolecular force is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion acting between atoms, ions, and other neighbouring particles. These forces are weak relative to the intramolecular forces that hold a molecule together.
Intermolecular hydrogen bonding is responsible for the high boiling point of water at 100 degrees Celsius. Water molecules have four active bonds, and this extensive hydrogen bonding gives water a far higher boiling point than the other group 16 hydrides, which have little capability to hydrogen bond.
The first reference to the nature of these microscopic forces is found in Alexis Clairaut's work Théorie de la figure de la Terre, published in Paris in 1743. Later scientists who contributed to investigating microscopic forces include Laplace, Gauss, Maxwell, Boltzmann, and Pauling.
The three contributions to van der Waals forces are the Keesom force between permanent dipoles, the Debye force between permanent and induced dipoles, and the London dispersion force from fluctuating dipoles. The London dispersion force is the dominant contribution because all materials are polarizable.
A hydrogen bond has a dissociation energy of about 4 to 50 kilojoules per mole, roughly 21 kilojoules per mole in water, making it stronger than dipole-dipole interactions at 2 to 8 kilojoules per mole. Ion-dipole bonding is even stronger than hydrogen bonding.
Intermolecular forces matter in biochemistry because all enzymatic reactions begin with a weak intermolecular interaction between the substrate and the enzyme. Several such weak interactions with the right spatial configuration at the active center restructure molecular energy states, breaking some covalent bonds and forming others to drive enzymatic reactions.