A cohort (from the Latin cohors, plural cohortes) was the standard tactical unit of a Roman legion and was composed of 360 soldiers. A Cohort is considered to be the equivalent of a modern military battalion. The Cohort unit replaced the manipular system following the reforms traditionally attributed to Gaius Marius in 107 BC. Until the middle of the first century AD, 10 cohorts (about 3600 men) made up a Roman legion.
Cohort (military unit) Wikipedia
During the 1st century AD, the command structure and make-up of the Legions was formally laid down, in a form that would endure for centuries. The first cohort was now made up of five double-strength centuries totalling 800 men, the centurion of its 1st century automatically being the most senior in the legion. This century was known as the primus pilii (first files), and its centurion was known as the primus pilus (first file or first spear). The Primus Pilus could be promoted to Praefectus Castrorum, or "Camp Prefect." The Praefectus Castrorum would be in charge of the daily running of a legion.
The other cohort consisted of approximately 480 men in six centuriae of 80 men, each commanded by a centurion assisted by junior officers. At various times prior to the reforms, a century might have meant a unit of 60 to 80. The cohort had no permanent commander; it is assumed that in combat, the most senior centurion of the six would have commanded the entire cohort. In order of seniority, the six centurions were titled hastatus posterior, hastatus prior, princeps posterior, princeps prior, pilus posterior and pilus prior (most senior).
These ranks followed the order of seniority in the earlier manipular legions, where the youngest and least experienced units were termed hastati, next principes, and the oldest and most experienced triarii (pilus was a rare alternative name for triarius, the singular of triarii).
The legion at this time numbered about 5,400 men, including officers, engineers and usually a small unit of cavalry (equites legionis; 120 men and horses).
Auxiliary cohorts could be quinquagenaria (nominally 500 strong) or milliaria (1000 strong).Cohors alaria: allied or auxiliary unitCohors classica: auxiliary unit originally formed of sailors and marinesCohors equitata (LA): unit of auxiliary infantry with attached mounted squadronsCohors peditata (LA): infantry unitCohors sagittaria: infantry auxiliary unit of bowmenCohors speculatorum (LA): guard unit of Mark Antony composed of scoutsCohors torquata (LA): auxiliary unit granted a torques (military decoration)Cohors tumultuaria (from tumultus, "chaos"): irregular auxiliary unit
Some paramilitary corps in Rome consisted of one or more cohorts, though none were part of a legion:The nine cohortes praetoriae, never grouped to a legion, the famous and infamous Praetorians. The term was first used to refer to the bodyguard of a general during the republic; later, a unit of Imperial guards (temporarily restyled cohors palatina, "Imperial Cohort", c. 300 AD, under Diocletian's tetrarchy).Cohors togata was a unit of the Praetorian guard in civilian dress tasked with duties within the pomerium (sacred center of the Capital, where all armed forces were forbidden).Cohortes urbanae, "urban cohort": military police unit patrolling in the capital.Cohortes vigilum, "watchmen": unit of the police force which also was the fire brigade in the capital.Cohors Germanorum (LA): the unit of Germani custodes corporis (imperial body guards recruited in Germania).
Furthermore, the Latin word cohors was used in a looser way to describe a rather large "company" of people (see, for instance, cohors amicorum).