Calenardhon was the first name of the plains of Rohan, when it was still a part of the kingdom of Gondor. The name, in Sindarin, means 'the Green Region' or 'Green Province,' and was an area of sparsely-populated grassy plains west of Anórien and north of the White Mountains.
This area of Gondor was of constant incursion, and, during the reign of the Steward Cirion, came under attack from the Balchoth. In order to drive back the invaders, Gondor called upon the Éothéod for aid; the horsemen, under Eorl the Young, were successful in vanquishing the enemy at the Field of Celebrant.
After the battle, what would become the people of the Rohirrim were ceded these lands by Cirion in return for their assistance in guarding the northern marches, as well as the Gap of Rohan, against invaders.