What is an "idol" in Islam?

The story of the teacher in Sudan whose kindergarten students named a teddy bear “Muhammad” raised this question. The NY Times website says that Islam prohibits the worship of idols, and that apparently the teddy bear was considered an idol.

Then I thought about the film “Hideous Kinky” where the young English woman makes dolls (with yellow yarn for hair) and tries to sell them, and gets a bad reception from people. I thought at the time it was because they were blonde.

But now I am wondering, was it because they were “idols”? Do girls in Islamic societies have dolls? Are children allowed to have stuffed animals, regardless of the name?

Well, I know there is an Islamic Barbie-type doll, for what that’s worth. She’s available veiled (I think it differs by country) and promotes Islamic values.

Found it! Fulla (doll) - Wikipedia