The skin of your teeth

Li: Hi, I'm Li, and welcome to The English We Speak. I'm here today with Jen.
Jennifer: Hi!
Li: You look a little ... flustered? Are you ok?
Jennifer: I woke up late and had to run to the train station. There's only one train an hour. I ran all the way there and made it by the skin of my teeth, just as the doors were closing. Phew! Is there any coffee ... ?
Li: Hang on ... how did your teeth help you to run for the train?
Jennifer: Sorry?
Li: You said "I made it by the skin of my teeth." I've got to see this! Show me your teeth! When did they grow skin?
Jennifer: There's no skin on my teeth. That would be disgusting. Yuck.
Li: So what did you mean?
Jennifer: If you do something 'by the skin of your teeth' it means that you did it by a narrow margin—so you just managed to do it, or almost failed.
Li: So, if you got to the train by the skin of your teeth, it means that you nearly missed it?
Jennifer: That's exactly right. Let's hear some more examples of the phrase in action:
Li: So when you just manage to do something, you can say you did it by the skin of your teeth?
Jennifer: That's it.
Li: That's a really funny phrase. I like it.
Jennifer: It's good to be able to get your teeth into English phrases like this.
Li: My teeth? What about my teeth?
Jennifer: It's just another phrase, silly. If you get your teeth into something, it means that you become really involved in it.
Li: Well in that case, I do love getting my teeth into a new phrase ... Teeth ... hang on ... Oh no! I've just remembered, I have a dentist's appointment at twelve o'clock—it's ten to twelve now, I'll never make it!
Jennifer: You go, I'll finish the programme—if you run you might make it, but by the skin of your teeth!
Li: Thanks Jen—bye ... 
Jennifer: Join us again for another edition of The English We Speak and visit our website, bbclearningenglish.com. Bye!