a cavalry unit consisting of two or more troops and headquarters and supporting arms
"The ancient commander inspected his squadron, verifying that every troop and supporting arm was ready for battle."
an air force unit larger than a flight and smaller than a group
"The new fighter squadron took off from the base to escort the supply flights across the border."
a naval unit that is detached from the fleet for a particular task
"The admiral ordered the squadron to detach from the main fleet and secure the harbor entrance before dawn."
Primarily, a square; hence, a square body of troops; a body of troops drawn up in a square.
"The Roman legion formed its defense into a tight squadron to withstand the enemy's charge from all sides."
In plain English: A squadron is a small group of people who work together as part of a larger organization, often used to describe units within an army or air force.
"The squadron flew in formation over the city during the air show."
Usage: A squadron is an obsolete military term referring to a formation arranged in a square shape and should not be confused with the modern meaning of a flight or patrol group. Use this word only when discussing historical tactics involving infantry squares, as it has no application for contemporary aviation units.
The word squadron comes from the Italian squadrone, which is an enlarged form of squadra meaning a square formation or group. It entered English to describe a military unit organized in such a block-like shape.