Not sure of the context in which the former President used the phrase, so it is hard to answer. Typically, it is used to give emphasis to some aspect of the "American idea." The United States is what is referred to as a "creedal" nation. (As Lincoln, put it rather famously, we "are a nation dedicated to a proposition.") That is that the idea of nationhood revolves around the acceptance of certain broad ideas - in the American context, typically those ideas articulated in the Declaration of Independence, the Constitution, the Bill of Rights, and sometimes famous speeches in American history like the "Gettysburg Address." This differs us from countries like Germany, Japan, China, etc, that tend to define nationhood with reference to a common language or ethnicity. (As President Reagan once put it, "You cannot be German-Frenchman or a Japanese-Italian, but you can be a German-American or French-American or a Japanese-American.") As to the "beating heart," it could be a reference to the American people. After all, ideas don't literally have "beating hearts," but people do. To the extent that Americans keep those ideas, it can be said that they are the "beating heart of the American idea." I must confess that, while not denying the reality of our creedal origins, I do think that too often that the idea is reduced to platitudes that become a substitute for actual real thought. As an example, you hear Senator McCain saying that good relations with Russia contravenes American principles. That is silliness on stilts. It is no more true than when we aligned with the USSR to defeat the Axis Powers during World War II. Perfect adherence to our ideals - indeed, even perfect agreement among ourselves on what those ideals are - is unlikely in an imperfect (and often dangerous) world. We are a creedal nation, but how we manifest those ideas is apt not always to conform to those ideals. There are those who would argue that such inconsistencies discredit our ideals. I sincerely doubt that those who lived under German occupation in WWII would quite see it that way.

"Beating heart" = the lifeblood. Its a metaphor.

My pleasure to be able to help. I am not sure when you responded since the system only notifies me when I get an "Answer" to one of MY questions. So my apologies for this late reply. I looked at Mr. Obama's speech, and his reference was a metaphor. He was saying that THE most essential thing - the very essence and defining idea that shapes everything else that flows from America's ideals - is the idea of citizen participation. So in a sense he was saying what I suggested in my initial reply - that the American people are what he is talking about. Specifically that people engaging in political and civic life is what makes American ideals vital and active. To use another metaphor, the American people "give life" to our ideals. Frankly, it is something of a banality expressed with an artistic flair, but he is not wrong. Hope that helps. My best as you learn to master English. I will say that, at least based on what you have here, your written English is quite good for a non-native speaker. My compliments.