What is the distinction between real and nominal GDP?

You need to be careful with this one. To add together all the many things that collectively represent a nation's output, we add up the value of each good's production. This means we measure GDP in dollars. Now, assume we use year 2002 prices to add all these things up, and get a number for GDP. We say we have calculated GDP "using 2002 prices". Another way of saying this is that GDP is calculated in "2002 dollars". 2002 is also referred to as the base year.
Now, in the base year, real and nominal GDP are exactly the same.
But, consider calculating GDP for 2003. We could use 2003 prices. Then, the growth of GDP from 2002 to 2003 will reflect both the increase in the quantity of goods produced and the increase in the general price level (inflation). When these effects are both included, we say we are calculating nominal GDP growth. 
But we could also have calculated GDP for 2003 using 2003 quantities, but 2002 prices. In this case, the growth in GDP from 2002 to 2003 only reflects the increase in the quantity of goods produced. This is what we call real GDP growth.
So, if the base year (the year from which the prices are taken) is different from the year in which we are calculating GDP, nominal and real GDP will differ by the amount of inflation that has taken place between the base year and the year of the GDP calculation.
Economists are generally interested in real GDP growth, because it tells us about how much wealthier we might be getting over time.