Context

Job speaks this line as he's telling his friends about all the terrible things that have happened to him...which takes a while, as you may recall.

Yes, Job is still alive, but only barely, by the thinnest margin—i.e., by the skin of his teeth. Then again, he is still alive, and later in this chapter, his tone becomes more hopeful. 

Though it was a close call, he's still here.

Where you've heard it

Anytime someone just barely escapes disaster or achieves victory, you're likely to hear someone use this phrase. "Did you pass your Topics in Metaphysics and Epistemology exam, Gertrude?" "By the skin of my teeth, Bob. By the skin of my teeth."

Very rarely will you hear this phrase used literally, unless you're planning on going into the very specialized field of dental dermatology.

Pretentious Factor

If you were to drop this quote at a dinner party, would you get an in-unison "awww" or would everyone roll their eyes and never invite you back? Here it is, on a scale of 1-10.

This one has become so common that all of its pretentiousness is used up. Good job, Job.