Answer: The main purpose of the speech was to get support from the citizens of the U.S. for the space program and their new goals.
In the following citation from the speech, President Kennedy speaks about the progress of the country and how the past achievements led to this new complex exploration of the human race that will mark history forever.
"If this capsule history of our progress teaches us anything, it is that man, in his quest for knowledge and progress, is determined and cannot be deterred. The exploration of space will go ahead, whether we join in it or not, and it is one of the great adventures of all time, and no nation which expects to be the leader of other nations can expect to stay behind in the race for space."