Hyperconjugation is the stabilizing interaction that results from the interaction of the electrons in a sigma bond (usually C-H or C-C) with an adjacent empty (or partially filled) non-bonding p-orbital or antibonding π orbital or an antibonding sigma orbital to give an extended molecular orbital that increases the stability of the system. Hyperconjugation can be used to explain phenomena such as the gauche effect and anomeric effect.
Orbital symmetry is important when dealing with orbitals that contain directional components like p and d.  An example of such an effect is square planar low-spin d transition metal complexes.  These complexes exist as square planar complexes due to the directionality of the metal center's d orbitals despite fewer steric congestion in a tetrahedral geometric structure.  This is simple one example of many varied examples, including aspects of pericyclic reactions such as the Diels-Alder reaction, among others.
Electrostatic interactions include both attractive and repulsive forces associated with the build-up of charge in a molecule.  Electrostatic interactions are generally too weak to be considered traditional bonds or are prevented from forming a traditional bond, possibly by a steric effect.  A bond is usually defined as two atoms approaching closer than the sum of their Van der Waal radii.   Hydrogen bonding borders on being an actual "bond" and an electrostatic interaction. While an attractive electrostatic interaction is considered a "bond" if it gets too strong, a repulsive electrostatic interaction is always an electrostatic effect regardless of strength.  An example of a repulsive effect is a molecule contorting to minimize the coulombic interactions of atoms that hold like charges.
Electronic spin state at it simplest describes the number of unpaired electrons in a molecule.  Most molecules including the proteins, carbohydrates, and lipids that make up the majority of life have no unpaired electrons even when charged. Such molecules are called singlet molecules, since their paired electrons have only one spin state. In contrast, dioxygen under ambient conditions has two unpaired electrons.  Dioxygen is a triplet molecule, since the two unpaired electrons allow for three spin states.  The reaction of a triplet molecule with a singlet molecule is  spin-forbidden in quantum mechanics. This is the major reasons there is a very high reaction barrier for the extremely thermodynamically favorable reaction of singlet organic molecules with triplet oxygen. This kinetic barrier prevents life from bursting into flames at room temperature.
Electronic spin states are more complex for transition metals. To understand the reactivity of transition metals, it is essential to understand the concept of d electron configuration as well as high-spin and low-spin configuration.  For example, a low-spin d transition metal complex is usually square planar substitutionally inert with no unpaired electrons.  In contrast, a high-spin d transition metal complex is usually octahedral, substitutionally labile, with two unpaired electrons.
Jahn–Teller effect is the geometrical distortion of non-linear molecules under certain situations. Any non-linear molecule with a degenerate electronic ground state will undergo a geometrical distortion that removes that degeneracy. This has the effect of lowering the overall energy. The Jahn–Teller distortion is especially common in certain transition metal complexes; for example, copper(II) complexes with 9 d electrons.
Trans influence is the influence that a ligand in a square or octahedral complex has on the bond to the ligand trans to it. It is caused by electronic effects, and manifests itself as the lengthening of the trans bonds and as an effect on the overall energy of the complex.