Anosmia is a lack of functioning olfaction

Olfaction

Olfaction is the sense of smell. This sense is mediated by specialized sensory cells of the nasal cavity of vertebrates, and, by analogy, sensory cells of the antennae of invertebrates...

, or in other words, an inability to perceive odor

Odor

An odor or odour is caused by one or more volatilized chemical compounds, generally at a very low concentration, that humans or other animals perceive by the sense of olfaction. Odors are also commonly called scents, which can refer to both pleasant and unpleasant odors...

s. Anosmia may be either temporary or permanent. A related term, hyposmia

Hyposmia

Hyposmia is a reduced ability to smell and to detect odours. A related condition is anosmia, in which no odours can be detected. Some of the causes of olfaction problems are allergies, nasal polyps, viral infections and head trauma...

, refers to a decreased ability to smell, while hyperosmia

Hyperosmia

Hyperosmia is an increased ability to smell - for example, being able to identify the perfume of the previous occupant of a chair. It is seen in patients with cluster headaches, migraines, and adrenal cortical insufficiency , although some people possess it naturally...

 refers to an increased ability to smell. Some people may be anosmic for one particular odor. This is known as "specific anosmia". The absence of the sense of smell from birth is called Congenital Anosmia.
Anosmia can be diagnosed by doctors by using acetylcysteine tests.