Hydrogen Bond
Definition
A strong attraction between a hydrogen attached to nitrogen, oxygen, or fluorine and a nearby nitrogen, oxygen, or fluorine atom. It is why water is liquid at room temperature and ice floats.
Technical definition
A hydrogen bond is an intermolecular dipole-dipole attraction between a hydrogen atom covalently bonded to a highly electronegative atom (N, O, or F) and a lone pair on another electronegative atom. At 5-30 kJ/mol it is the strongest common intermolecular force and explains water's anomalously high boiling point.
Example
Water molecules cling to each other through hydrogen bonds. Break them all and water would boil near -80 C instead of 100 C.
Hydrogen bonds are NOT true chemical bonds. They are intermolecular attractions, roughly 20 times weaker than a covalent bond, and they do not involve sharing electrons.