This candy was around long before the song of the same name. It is basically individual pieces of very cheap and sweet fruit-flavored taffy, with a taste similar to Starburst. By that I mean normal original Starburst not the weird liquid ones. But you get a little bonus with the Laffy Taffy. There is a different joke on each tiny Laffy Taffy wrapper. Most are pretty corny, which is even better.
The flavors vary in the bag: grape, cherry, etc. I have also seen them in tropical flavors, like banana. I don't think any of them actually taste like the fruit they are supposed to represent. It is kind of like how "purple drink" tastes like grape. I am not a big fan of this candy, but my boyfriend would eat only these if he could subsist on them. I think they taste like gum after it has lost most of its flavor, and they also get stuck in my teeth.
It's only like 3 bucks for a huge bag of Laffy Taffy, so you might as well try them if for nothing else than the jokes. Maybe you'll get some good stand-up material from reading the wrappers.