It is how often a single dollar is traded for new goods and services in a given year. This means that if $ 50 were traded between individuals for goods and services, in a closed economy, over the course of the year, and the sum of all those transaction resulted in $ 200 in the course of a year, the velocity of money was 4.
Reasoning alone would lead us to determine that the higher the velocity of money the higher the inflation rate, this view is supported by economists who favor the quantity theory of money, however, both Keynesian and Austrian economists have criticised the quantity theory of money.
One criticism is that the quantity theory, while true in the long run, in the short run it is not necessarily true because vendors don't want to raise prices for their customers. My dispute with this argument is just because a vendor doesn't raise his price initially doesn't mean there isn't inflation, it just means that the vendor has elected to absorb the real value loss for the time being.
As for the Austrian economists, there are two criticisms, one from Hazlitt and one from Mises. Hazlitt argued that the equation failed to account for the psychological affects that determine the value of the currency. He argues that prices initially increase at a smaller rate than the initial increase to the money supply but after a period of time the price increase will increase by a greater amount than the increase of the money supply. Mises criticism of the quantity theory of money is that, ultimately, it is does not stem from the actions of the individual, essentially a top to down approach versus a bottom up.
Ultimately I don't think either Hazlitt or Mises disagree with the principal that increasing the money supply would result in inflation over time; however, I believe their disagreement is stems from the fact that
a. It doesn't account for the psychological affects of inflation or deflation on individuals
b. That it is a top down approach versus a bottom up approach.
There is also the point I made earlier that inflation doesn't increase uniformly across the board. Once again the real estate bubble. The Fed's easy money policies lead to an abudence of money, via cheap credit, which, when coupled with short sighted government policies and programs, such as the FHA, Fannie May, equal opportunity lending and the like, lead to an inflationary bubble within the residential real estate sector. The affects on prices were not that large, at least according to official CPI estimates:
Years Avg Inflation
However, during the two peak years of the bubble and with it's initital collapse, the periods of 2005 to 2008, average inflation was 3.3 percent. Now is this alone indicative of a massive bubble? No, inflation of around 3% is within the target rate set by the Federal Reserve, but it is higher than the preceding period, however, I think there are two reasons why this is the case:
1) The easy money effects also created an above average inflationary effect in the stock market and profits from real estate sales made there way into those markets.
2) By virtue of having our nation's reserve currency status, and being the largest consumer of imports in the word, this allowed us to export our inflation. Exporting, not wanting the prices of their goods to rise in America, would devalue their currency accordingly in order to maintain a good currency exchange rate. This helped their exports, however, it meant that their currency would also inflate and result in more expensive goods for their own people.
In the end, whether or not we exported our inflation or not, and whether or not velocity of money is a good indicator of inflation or not. The fact is, that fundementaly, the amount of money in our economy that is in excesses of our production will eventually result in inflation. We may not be able to always accurately measure this phenomena, however, historical analysis has shown this to be an emprical truth. Mo' money means Mo' problems.