Cask ales are unfiltered and unpasteurized ales that are designed to undergo a secondary fermentation in the cask, which will produce some natural carbonation. A lot of people refer to them as real ales because the carbonation comes form inside the beer itself instead of being forced into it from a gas system, which is what you use when you have a draft setup like this.
Cask ales are served, usually from a hand pump, which will force air in and cause the beer to come out, so it's a very mechanical, natural process. If you order a cask beer, you're going to have the experience that it is significantly less carbonated than a beer that you would get out of a draft system that uses CO2 and nitrogen. And it's also going to be a little less cold, usually around 55 degrees.
And this is going to cause a lot of the flavors in the beer to come out. SO the slight warmth from it and the lack of any gas being pushed through it will really allow you to taste what's in the beer itself. I really encourage you to give it a try, but just have different expectations. You don't want to be expecting what, to you, might be a normal draft beer, when you order a cask ale. But just open your mind and think, 'am I getting more flavor from this? Do I enjoy this?' And if you do then it might be a whole new world of beer that's been opened up for you.