Besides just being a great speech technique, Reagan was emphasizing that the American commitment to protecting West Germany and West Berlin was unchanged from the early 1960s when Kennedy made his speech. Kennedy's point was to show solidarity with our German allies in the wake of Soviet construction of the Berlin Wall, his own speech reiterating the commitment Harry Truman had made during the Berlin Airlift in 1948-49.
Reagan was all about symbolism, and in addition to boosting the morale of Germans, he was also issuing a challenge to Soviet leaders to bring down the Iron Curtain and allow Germany to be reunified. I don't think he believed it would happen anytime in the near future, but as another speech in front of the Brandenburg Gate made clear, ("Mr. Gorbachev, tear down this wall!") Reagan considered the Germans one of our closest allies.