The word itihAsa splits as iti-ha-Asa and means thus-verily-happened. Therefore itihAsa means history as it truly happened.
Many texts of Sanatana Dharma record history - just in a form that is different than what is now considered to be the norm. Today, the definition of History is that which was introduced into India by the British. Much prior to that, the sages recorded history so that future generations could benefit from its learnings. The Rigveda has recorded some history, the Ramayana of Valmiki and the Mahabharata by Sage Vyasa are popular examples of Itihasa.