This post not about the main part of this address, although as its my area and interesting I may write about it later. Instead I’m going to talk in a non-technical way about its premise, because that alone has implications that may be well known among economists but not elsewhere. The following is based on his presentation.
Should governments worry about temporarily paying for things by borrowing? One standard answer is yes, because although nothing obliges government to pay off this extra debt (it can be rolled over), it has to pay interest on that debt which requires higher taxes. If the government didn’t raise taxes to pay the interest on the debt, but instead just borrowed more to pay the interest, you would enter what is sometimes called a debt interest spiral, where debt goes up and up and eventually explodes.
But does a slow explosion in debt matter if the economy is also growing? A government (like a firm of individual) should look at debt as a ratio to its ability to pay, and the easiest way to do that is to look at the debt to GDP ratio. A company would not worry about increasing debt if its profits were rising even faster. For a given stock of debt, its growth rate is given by the rate of interest on the debt. So GDP rises faster than debt if its nominal growth rate (real growth plus inflation) is greater than the rate of interest on that debt. In shorthand, g > r.
Typically economists like me tend to assume that this is not true, and instead r > g. But the starting point for Blanchard’s lecture is that currently, and on average in the past, g > r. There has been only one decade since the 1950s when this hasn’t been true, and that is the 1980s when governments were pushing up interest rates to bring inflation down. Most of the time g > r. So the fact that g > r today may be the rule and not an exception.
Why do economists typically assume r > g when the opposite has generally been true? One answer is called financial repression, which is a label given to attempts by governments in the past to keep interest rates ‘artificially low’ in conjunction with various credit controls. The idea was that in a financially liberalised world where interest rates are used by central banks to target inflation there will be no financial repression, and real interest rates will be higher. So it made sense, the argument went, to assume r > g from now on even though g > r in the past. However what economists call secular stagnation suggests that the average interest rate required to keep inflation constant has actually been steadily falling, so Blanchard’s findings become relevant again. There is plenty of scope here for more research and debate.
So if normally g > r, does this mean we do not need to worry about debt? Not quite. What it means is that one of the standard objections to raising debt, which is that taxes will have to rise to pay the interest, no longer holds if g > r. If g > r the government can borrow to pay the interest, and yet the debt to GDP ratio will still gradually decline, because the economy is growing faster than debt. The objection to raising debt that taxes will have to rise in the future to pay for it disappears. Indeed the whole ‘burden on future generations’ objection to raising debt falls away, because the debt to GDP ratio declines by itself: there is no future burden.
An important proviso, however, is that we are talking about one-off increases in debt. Such one off increases would include, for example, increases in debt to build new public infrastructure or increases in debt caused by fiscal expansions to fight a recession. g>r does not mean we do not need to worry about persistent primary deficits (by which I mean spending permanently higher than taxes). A persistent primary deficit will add to the growth in debt, so the debt to GDP ratio will rise despite g > r.
This is just the starting point for Blanchard’s lecture, and if you are an economist I recommend watching it as it is very easy to follow. In policy terms I think it is the last nail in the coffin of what Paul Krugman calls the deficit scolds. Those who argued for austerity because of the burden on future generation, although on weak ground even if r > g, find their argument collapses if g > r. 
 Blanchard shows this remains true even if there are periodic shocks where r > g, as long as on average g > r.