What was Stephen trying to convince Israel of in his sermon?

Les explains that Stephen's whole purpose in this sermon is to bring the nation of Israel to the knowledge that the one they had killed was the King. This is the whole premise of these early chapters of Acts. Stephen draws a parallel with Moses, who at forty supposed his brethren would understand that God, by his hand, would deliver them out of Egypt, but they understood not. In the same way, Christ came to the nation the first time and presented Himself as their Messiah and King, but they never comprehended who He was—only a precious few did. Stephen therefore presses Israel to recognize that the one they killed was indeed their King.