What does Itihasa mean? Also, why no other text is classified under Itihasa except these two?
Iti-ha-asa means This has happened. Iti means This; ha- aasa means has happened really; Itihasas are the stories which really happened once in the past. They are not myths. Ramayana and Mahabharata are called itihasas as they really happened many years ago. Sometimes puranas are considered as itihasas because many believe that stories and incidents in the puranas are true and even there are people who think puranas are misinterpretations.
But the above is the meaning of Itihasa and it is right.
For the learned and the unlettered alike in our country the Rāmāyaņa and the Mahābhārata have for centuries been like their two eyes, pointing to them the path of dharma. The two poetic works are not included among the Purāņas and are accorded a special place as "itihāsas".
"Itihāsam" = "iti-ha-asam" (it happened thus). The "ha" in the middle means "without doubt", "truly". So an "itihāsa" means a true story, also a contemporary account. Vālmīki composed the Rāmāyana during the lifetime of Rāma. Vyāsa, author of the Mahābhārata, lived during the time of the five Pandavas and was witness to the events narrated by him in his epic.
"Pura" means "in the past". That which gives an account of what happened in the past is a "Purana", even though it may contain predictions about the future also. The term can also mean what was composed in the past. The genre called "novel" written in prose came after a long period in literature dominated by poetry and drama. When the novel was introduced into India it came to be called "navīnam". If "navīnam" means new, purāna means old.
A Purāņa must have five characteristic features – (lakshanas). The first is "sarga" (creation of the cosmos); the second is "prati-sarga" (how eon after eon it expanded); the third is "vamsa" (the lineage of living creatures beginning with the children of Brahmā); the fourth is Manvantara (dealing with the ages of the 14 Manus, forefathers of mankind during the 1,000 caturyugas), and the fifth is "vamsānucarita" (genealogy of the rulers of the nation including the solar and lunar dynasties). Besides there are descriptions of the earth, the heavens, the different worlds.
In the Purāņas Vyāsa has dealt with the stories or events of the past which of course is in keeping with their name (that is "Purāņas"). But how? Vyāsa could see into the past as he could into the future. So what he has written of the past must be an eyewitness account. However, his contemporaries would not have known about them. The Mahābhārata and the Rāmāyana are different. When these works were first made known to the world most people must have been familiar with the characters and events described in them. There is thus no reason to doubt their authenticity. The "ha" in "itihāsa" confirms this.