Kennedy sought to inspire patriotism in evoking the Founding Fathers, recalling such phrases as "inalienable rights" and "freedom" to a populace faced with threats to their way of life with Communism on the rise and to the possiblity of a better one through Civil Rights. By alluding to the country's "forbearers," Kennedy aligns himself, making his efforts seem in accord with the Constitution--a good strategy, although not entirely honest.
Also, JFK was trying to gain support for what he intended to do in foreign affairs. He was trying to say "look, I'm just like the Founders. The things I want to fight for around the world are just like what they fought for." By invoking the "forebears" he is claiming that what he is doing is nothing new, but is in fact an extension of the American Revolution.
By saying this, he is trying to get people to have a positive emotional attitude towards him and towards the policies that he will try to enact during his time in office.
"Forebears" means ancestors. By invoking the memory and stature and wisdom of those who "prescribed" the "solemn oath" used to swear new presidents into office, President Kennedy was connecting his new administration with all the history and accomplishment of preceding administrations. He was hoping to emphasize a connection with values upon which the United States was founded - "the belief that the rights of man come not from the generosity of the state, but from the hand of God." In the midst of the uncertainties and threats found in political and economic situations within the US and around the world, JFK hoped to rally the support of the American public behind his presidency as the newest in the long line of patriots who had led the nation wisely in previous years.