Electrostatics is the branch of physics and chemistry that deals with the way static electrical charges behave. This is in opposition to the study of electrical currents, which is what is most commonly denoted by the term "electricity".

An atom consists of a positively charged nucleus and the negatively charged electrons that orbit it. Since they have opposite charges, they attract, and the atom has an over-all neutral electrical charge. For example, let's take a very simply atom, helium:

       He
Wow, that is underwhelming. Since Helium has no electrical charge, it for the most part neither repels or attracts other atoms or molecules. However, the nucleus and electrons of a helium atom are still oppositely charged, so it still has some electrical charge, and there is still a tiny amount of electrical attraction that "peeks out" from the nucleus to other electrons. So, for example, if you have two Helium atoms, the nucleus of one is going to have a slight attraction to the electrons of another. This attraction is called Van Der Waals bonds, and it is very weak. Weak enough that at any temperature above 5 kelvin (5 degrees above absolute zero), Helium is in a gaseous form. Lets look at something more interesting, a simple molecule made out of two elements: methane.
          H   H
           \ /
            C
           / \
          H   H
In a methane molecule, the carbon and hydrogen atoms are bonded by covalent bonds, meaning they are sharing electrons. In this particular molecule, they are sharing the electrons about equally, meaning that the electrical charge is distributed equally across the molecule. For this reason, Methane also is gaseous down to a very low temperature. of about 110K, or -180C.

Lets look at a more interesting, and very important molecule: water.

        O
       / \
      H   H
In a water molecule, the oxygen atom is hungrier for electrons than the hydrogen atoms, so the molecule is not electrically neutral. Instead, it is focused on one side. We could draw the water molecule like this:
       - - 
        O
       / \
     +H   H+
And since opposite charges attract, if two water molecules are close together, they will do this:
            - - 
             O
            / \
          +H   H+
            \  /
             - -
              O
             / \
           +H   H+

And so on, the pattern can repeat. The bond between the negative oxygen and positive hydrogen, called a hydrogen bond, is not as strong as a covalent bond, but it is strong enough. Although methane and water have about the same weight, the hydrogen bond is strong enough to keep water in a liquid state up until 100C: 260 degrees celsius hotter than the boiling point of methane.

Some atoms lose their electrons entirely, losing their net neutral charge. For example, table salt is made out of Chlorine and Sodium atoms that have gained and lost an electron, respectively, and then are drawn to each other by their electrical charges. Many organic molecules in the body also have some type of ionic charge on them.

To return to the subject of Van Der Waals bonds, I wrote that the electrical attraction between two electrically neutral molecules is very low, and this is the case, but as the molecules get larger, those attractions build up. Methane is the simplest and smallest hydrocarbon, but as they get larger, the electrostatic attraction between two hydrocarbons gets larger. For example, here is two hexane molecules (with the hydrogen atoms omitted to save space):

C-C-C-C-C-C
C-C-C-C-C-C

At this size, the slight electrical charge between net-neutral molecules is getting strong enough to overcome kinetic energy: the boiling temperature of hexane is 70C, well over room temperature.

Organic molecules can get quite large and complicated, with electrical charge distributed in many places. These bonds, although slight on their own, add up until the electrostatic attraction between one molecule can bind itself to another molecule. A large organic molecule might have many atoms whose "shape" fits into each other, complimented by sites where hydrogen bonds and ionic bonds attract the two molecules towards each other. It is these bonds that allow molecules to interact, and make metabolism and life possible.

One caveat should be made in understanding the nature of electrostatics. Even for those who have resources beyond ASCII art, the graphic depiction of molecules can be deceptive. For example, my drawing of methane was on a plane, but an actual methane molecule is three dimensional, with the hydrogen atom at the corners of a tetrahedron. Many times chemical formulas don't give a sense of the actual size and shape of the atoms involved, and the inherent "muddiness" of the electrical charges involved. Atoms are not billiard balls. At the scale of atoms, many of our normal conceptions of the physical world break down. It is due to this unseen and somewhat amorphous nature of electrical charge that guessing how molecules really fit together and interact is very tricky, and why electrostatics is one of the many fields that make organic chemistry impossible to totally understand.