What is Real Ale?
The phrase 'Real Ale' was coined by CAMRA, the campaign for Real Ale.
It's also referred to as cask-conditioned beer / cask ale. What it means is unfiltered and unpasteurised beer that is served cask-conditioned (ie the beer is still brewing in the cask - this is known as secondary fermentation) and served from a cask without gas assistance. These days it can also refer to bottled beer where the beer is bottle-conditioned (secondary fermentation).
In 1970s Britain, breweries moved towards keg ale which had been filtered, pasteurised and carbonated. The benefit to the breweries was that keg ale keeps for much longer than cask ale as it's no longer 'live' so was suitable to sell to more pubs, given the media-led push in the 1970s towards getting people to drink lager led to lower demand for beer in many pubs.
In short, if your beer is not served from a handpump that someone has to pull, the chances are, it's probably not real ale.
Real ale should be relatively flavoursome compared to keg ale and should not have a metallic taste unlike certain keg ales! Real ale in Great Britain is generally served at a warmer temperature than keg ale ('British Cellar Temperature' is 55 degrees Farenheight or 12.77 degrees celsius.) - the reason for this is the subtle aromas and flavours you get in real ale are more readily noticed when it's not too cold. The nastier and cheaper flavours in lager and keg ale tend to be supressed by cold serving temperatures.
Bottle-conditioned Real Ale
Real ale can also come in bottles these days. Like a vintage wine, it comes with sediment, and you'll need to decant carefully if you don't want the yeast sediment in your beer glass. It'll do you no harm to drink the yeast incidentally, in fact it's packed with nutrients but it will do its best to ferment in your stomach before being digested, so there may well be gaseous side-effects... Bottle-conditioned beer tends to keep for a long time, with its flavour steadily and subtly improving over time.
Generally the 'best before' on bottled real ale is about five to six months. It should still be drinkable long after that (compared to pasteurised bottled beers) but will be past its prime.