Refers specifically to an army division as a military unit. Not used for other meanings of 'division' such as corporate departments or mathematical division.
その師団は前線に配置された。
The division was deployed to the front line.
He was assigned to the 7th Division.
He belongs to an infantry division.
新たに一個師団を編成した。
They newly organized a division.
The new soldiers were assigned to their respective divisions.
連隊 is a regiment, a unit smaller than a 師団 (division).
軍団 is a corps, a larger formation made up of multiple 師団 (divisions).
師団 refers to a division, a smaller military unit than 兵団 (a corps made up of multiple divisions), so the two are easily confused in scale.
師団 is a division, a military unit larger than a 旅団 (brigade), so the two are easy to confuse when learning military rank terms.
team of doctors; medical team
division commander
infantry division
airborne division
From 師 (し, 'teacher; military unit') + 団 (だん, 'group; corps'). The kanji 師 historically referred to a military unit of 2,500 men in ancient China, later adapted in Japan for the modern army division.