The Campaign for Real Ale defines it as,
"beer brewed from traditional ingredients, matured by secondary fermentation in the container from which it is dispensed, and served without the use of extraneous carbon dioxide"
The bottled beer that most homebrewers keep and serve would be considered "Real Ale" under this definition. If you keg your unfiltered beer, and add primings to carbonate the beer, that would be considered "Real Ale". However, the conditioning and dispense of real ale, or cask ale, is different. Real Ale goes through a process known as venting whereby the ale is opened and allowed to breathe. Co2 escapes, and the beer is brought into "condition". This is where the art of the cellarman lies. Given enough time, the ale would lose it's condition and eventually go stale and sour. The cellarmans job is to get the condition just right, then either close the cask with a hard spile, or if deemed ready put it up for sale. A few hrs. here makes a big difference!
Real Ale, or as we'll call it from here on out "Ale" is the English style many consider "warm and flat". A properly served, conditioned pint of Ale will never be warm or flat, but in comparison to other styles it certainly is.
I'll never forget my first cask ale. It was a moment that literally changed the course of my life and opened my eyes to a world outside the narrow world I had been living in.