Jupiter is both the "fixer" and the "mediator" in this epic poem. He fixes things for the Trojans by promising them a legacy. He steps in to fix the problems created by his wife and his daughter, who are at odds in Aeneas' legacy. He, literally, puts out fires and steps in to restore the promised destiny. After Aeneas and his crew finally arrive in Italy, Jupiter must order his wife (Juno) to stop interferring in the fate of these people. In order to secure her promise, Jupiter must compromise, and promise that the Trojan descendents will create a culture that incorporates the Latin ways. In other words, he mediates to make a peace not only with his wife, but with the two warring cultures.
Jupiter was to the Romans as Zeus was to the Greeks, king of the gods. While many gods fought against each other, Jupiter is seen as a sort of referee who is more identified with the impersonal forces of fate. In the Aeneid, Jupiter therefore is portrayed as mature and levelheaded as he keeps Aeneas on track in the fulfillment of personal destiny. Behind all of this is the fact that since Jupiter, in Roman mythology, is the father of Mars, he is therefore the grandfather of Romulus and Remus, the founders of Rome.
When we consider that Vergil wrote this epic for Augustus, as a means of legitimizing his succession and reign of the Roman Empire, it is quite appropriate we find Jupiter as a central deity to the underlying motive of the Aeneid.