When hydrogen is bonded to a highly electronegative atom, such as oxygen, nitrogen, or fluorine, a partial positive charge is created on the hydrogen and a partial negative charge is created on the electronegative atom.  This enables the hydrogen to bond to the electronegative atom of a neighboring molecule and thus create a hydrogen bond.

A hydrogen bond occurs when hydrogen is bonded to an electronegative atom in one molecule, such as an oxygen, fluorine, or nitrogen, and then is attracted to an electronegative atom in another molecule.  The hydrogen has a partial positive charge and is attracted to the partial negative charge of the neighboring atom as seen in the image below.

This diagram shows how hydrogen bonding occurs between two water molecules.

In the diagram, the molecule on the left would form hydrogen bonds with another molecule of the same type because the hydrogen is joined to a highly electronegative atom, in this case oxygen.  The molecule on the right will not form hydrogen bonds because the hydrogens are only attached to the carbons and not the oxygen.  The difference in electronegativity between carbon and hydrogen is not large enough to create partial positive charges.

Hydrogen bonds are much stronger than other intermolecular forces.  They have greater polarity which means that it takes more energy to break apart these bonds and thus they have higher boiling points.  Water, H₂O, contains hydrogen bonds and has a boiling point of 100 degrees Celsius while phosphorus trichloride, PCl₃, contains dipole-dipole forces and has a boiling point of 76 degrees Celsius.  Molecules containing only London forces, such as  Fluorine- F₂ have very low boiling points.   This particular substance has a boiling point of  -269 degrees Celsius.