GDP, gross domestic product, is the measure of the economic activity carried out in an economy over a period of time. Economic growth is one the government’s four macroeconomic objectives which makes GDP an extremely important measurement. Recession is two quarters (6 months) period of negative growth; GDP is one of the first indicator to tell us we are in recession/ or we are out of recession. 
Economic growth links to the quality of life; an efficient and more productive economy is likely to provide a higher quality of life (note: quality of life is different to happiness). This makes economic growth important hence why governments make sure GDP isn’t negative. On the flip side, if economic growth is too high this can cause issues too. For example, there is likely to be higher inflation which leads to a bunch of other problems.
Moreover, there is another issue concerned with economic growth and that is, once we have reached a certain stable growth is it really important to be continually expanding? Is there a limit which economist fail to see? Could we not keep to a sufficient level of GDP and then spend time and money helping third world countries increase their GDP? The video below (not created by me) uses an interesting metaphor when describing too much economic growth:

Rather than working out all the products of an economy and researching their prices, GDP is measured by the amount spent on them. Since there are four key players who buy the output; the formula to work out GDP = Consumer expenditure + business investments + government expenditure + net exports.  Consumer expenditure is the largest group, in USA alone 70% of expenditure comes from there. Businesses need to buy mainly capital goods, government need to buy products so that they can fulfill their job (e.g. street lighting) and foreigners spend money through exports. (Note: we use net export figures rather than export so we can get a more accurate figure).

Real and Nominal GDP

Nominal GDP is a measure of GDP through that method; nothing is done to the values. These figures are raw data. However, this value is if you like skewed because of inflation. Inflation is a persistent rise in price levels.  If inflation rises by 10% and productivity rises by 2%, your raw GDP level would by 12%. However, from that you wouldn’t know whether the price level has risen or productivity has increased. That’s why we use real GDP measurements. This is simply nominal values minus the inflation. So we can get the true increase or decrease of GDP.
Inflation is typically measured through CPI (consumer price index) and RPI (retail price index). However, this is not measurements we can use to get real values. This is because GDP as mentioned before is measured by looking at expenditure of 4 groups of people and CPI and RPI seems to mainly covers inflation of consumer based products. So we use a measure of inflation called GDP deflator, this contains a wider range of products and get a more accurate value.
The formula to calculate Real GDP in this respect is quite easy, if you are good at maths in this respect:

Real GDP = Nominal GDP       X 100

         GDP Deflator