The Roman army used the phalanx as a attack formation until they realized the futility of the phalanx on un-level ground during a battle with the Samnites in 315 B.C. The consuls decided to create a more flexible system as a result the manipular formation was born. Later, the manipular system was replaced by the cohort system.
The drawing above compares the manipular system with the cohort system.
In Republican times, the Roman army marched toward the enemy in three lines Hastati, Principes, and Triarii. A legion would contain 10 maniples of each of the three types as its infantry component.
The cohort system was adopted at least partly in response to the difficulty fighting barbarians. The Celts and Spaniards were able to defeat a highly trained army because of their concentrated charges. The way to counter them was to concentrate men, in formation, on the Roman side: building cohorts out of maniples.