A menthol cigarette is a cigarette flavored with the compound menthol, a substance which triggers the cold-sensitive nerves in the skin without actually providing a drop in temperature.
Menthol cigarettes have also been shown to inhibitnicotine metabolism, causing "systemic enhancement in exposure to nicotine".
A menthol tastes minty - I'm sure you've chewed gum, I suppose if you set fire to a packet of Airwaves and try to smoke it, it'll taste similar, besides the presence of tobacco/nicotine etc - not that I'm suggesting anyone try this. Heck, please don't. I imagine it to be a rather unpleasant experience.
Anywho, in a regular cigarette you merely taste the tobacco and no mintiness.
The menthol ones seem a bit easier on the throat though, perhaps it's something to do with the menthol inside it, not so sure. Personally, I stick to regular cigarettes, had a menthol before though and it just tasted weird in comparison.
Although, if I were you I'd discard the whole idea. Smoking is bad for you.