It’s self-explanatory, really. It’s both a game and a book. I mean it can be both.
Ever played a game call Choices: Stories You Play? I would considered that game to be an interactive-story. You have many different stories to play, and in each story, you’ve got choices you can make to influence the course of the story.
On the other hand, there’s this so-called “Choose Your Own Adventure Series,”, where, just like its name implies, you can choose which path you want to take to arrive at the different conclusion. This one is also an interactive story, a combination of books and games, books you can play.
Reading books make you feel like you’re living another life, which is why it’s so fun to read. But it’s not as fun as when you really have a total control of where you want things to go. Sometime the protagonist do something you don’t like, but in the interactive-story, you can choose what the protagonist would do. It’s freedom. It’s fun.