Where $P_t$ is the price level at time $t$
This formula is just the percentage change in price.
A measure of economic growth from one period to another expressed as a percentage and adjusted for inflation (i.e. expressed in real as opposed to nominal terms). The real economic growth rate is a measure of the rate of change that a nation's gross domestic product (GDP) experiences from one year to another.
So inflation concerns itself with the changes in prices over time. Price can be measured by something like the CPI (consumer price index). GDP on the other hand focusses on what can be produced. If you look at the definition, you can see that in calculation real GDP, the inflation rate is essential. Real GDP is GDP controlled for inflation Useful when comparing different years.
An increase in inflation can be a driver for increased nominal GDP but not for increased real GDP.
This site provides a pretty solid background and isn't too hard to folow..