In this portion of his acceptance speech, Kennedy is comparing the people of his day to the pioneers who moved west during the period of westward expansion.  He is saying that these pioneers were brave enough to let go of their doubts and worries and strike out to conquer new lands.

Kennedy is referring to these pioneers because he wants Americans to step out into a "new frontier."  This new frontier will be one that is not physical or geographical.  Instead, it is a mental frontier.  He is challenging Americans to be like those old pioneers and to step up and change the world.  He wants them to confront and conquer

uncharted areas of science and space, unsolved problems of peace and war, unconquered problems of ignorance and prejudice, unanswered questions of poverty and surplus.