half of the terrestrial globe
"The northern hemisphere experiences summer while the southern hemisphere is in winter."
either half of the cerebrum
"The surgeon carefully mapped each hemisphere of the patient's cerebrum to ensure no vital functions were damaged during the procedure."
Half of the celestial sphere, as divided by either the ecliptic or the celestial equator .
"The ancient astronomers mapped the stars within each hemisphere defined by the celestial equator."
In plain English: A hemisphere is half of a sphere, like cutting an orange exactly in two from top to bottom so each piece has a round curve on all sides except where they were cut apart.
"The sun rises in the eastern hemisphere and sets in the western one each day."
Usage: In astronomy and geography, this term refers specifically to half a sphere rather than just any rounded area. Avoid using it casually to describe one side of an object unless you are discussing celestial bodies or planetary divisions.
The word hemisphere comes from the Latin hemisphaerium, which was borrowed from Ancient Greek. It is formed by combining words meaning "half" and "sphere."