Brief Summary
The Set-Up
It's 1987, and the Cold War has the world roughly divided into two camps: the Eastern communists and the Western capitalists. U.S. President Ronald Reagan was scheduled to make a brief trip to West Berlin and speak in front of the Berlin Wall; he knew his remarks would be heard by Westerners as well as many Easterners, and his speechwriter, Peter Robinson, worded the speech accordingly.
The rest is speech-making history.
The Text
The "Speech at the Berlin Wall," or "Tear Down This Wall!" as it's known to its friends, mainly addressed four topics.
First, it underlined the United States' support for West Berlin. Second, and most popularly, it urged Gorbachev to, well, tear down the Berlin Wall. This wasn't just an appeal to remove the physical wall itself, but to also remove the invisible-but-no-less-real divide the wall represented between the West and the East. Third, this speech outlined specific ways in which the Eastern and Western worlds could improve their relationship and make nicey-nice.
Finally, this speech delivered a message of freedom and prosperity, and it delivered it not only to the West, but also to any Easterners who were listening. (Clever.) Every word of a presidential speech is worried over, reviewed, edited, and subject to approval before it is delivered; this speech, though delivered to an audience of West Berliners and Western supporters, was also carefully crafted for its Eastern audience, those behind the Iron Curtain.
TL;DR
Reagan gets up in front of a German landmark and basically says, loud enough for the whole wide world to hear, that the Berlin Wall is stupid, communism is a big fat fail, and freedom is the answer to every question ever asked.