Nominal means "in name only," and a nominal price means the price of something in terms of a currency, like dollars.
Real prices means the price of something in terms of its actual value. For example, when we stopped using silver coins in 1964, the price of gas was 30 cents a gallon, or a little more than a silver quarter (25 cents). Today (November 2012), the price of gas is about $3.25 per gallon, and a silver quarter costs about $5.50. In other words, gas was worth more than a silver quarter in 1964, but it is worth less than a silver quarter today. So, in silver terms, gas is now cheaper today than it was about 50 years ago. The same thing is true if you look at the price of gas in terms of how many hours you would have to work at a job to earn enough money to buy a gallon of gas.
There is a lot of debate over what is considered a "real" price, and governments usually try to estimate real prices against a large number of goods called a "basket of goods," and even then, each government uses a different basket, with food being the most important thing in some countries, and electronics and cars being most important in others. Whatever case you use, you can "adjust today's prices for inflation" against a single good like gold or labor, or against a lot of goods, and then see how today's prices are really rising, or if the rise is mainly due to inflation.
With that in mind, here's the amazing part: for the last 100 years, real prices have generally gone down while nominal prices have gone up. For example, cell phones were once only a luxury for a few rich businessmen. But, with advances in technology and good business, cell phones became cheaper and cheaper to the point that cell phones can be found all over the world, and at almost any income level worldwide. This same change has actually happened with everything, with cell phones and electronics being the most obvious case, but even expensive things like cars require far less work to earn now than it took long ago (2 years of work in 1905, 8 months of work in 2005), which is a great thing. All of these advances came because entrepreneurs work with scientists and engineers to create new or improved products at lower prices, over and over again.