In chemistry an unpaired electron is a electron that occupies an orbital singly, rather than as part of an electron pair.
As the formation of electron pairs is often energetically favorable, either in the form of a chemical bond or as a lone pair, unpaired electrons are relatively uncommon in chemistry, because an entity that carries an unpaired electron is usually rather reactive. In organic chemistry they typically only occur briefly during a reaction on a entity called a radical; however, they play an important role in explaining reaction pathways.
More stable entities with unpaired electrons do exist, e.g. the oxygen-molecule has two unpaired electrons and the NO molecule has one. According to Hund's rule the spins of unpaired electrons are aligned parallel and this gives these molecules paramagnetic properties.
The most stable examples of unpaired electrons are found on the atoms and ions of lanthanides. The incomplete f-shell of these entities does not interact very strongly with the environment they are in and this prevents them from being paired. The ion with the largest number of unpaired electrons is Gd3+ with seven unpaired electrons.