Oh! Ok, a quine is

a computer program which takes no input and produces a copy of its own source code as its only output.

If you understand how to write a quine and you understand how the diagonal lemma works, you will find that the two concepts are basically the same thing. "Quine" is more of a computer science term than a mathematical logic term, so not all expositions of Gödel's incompleteness theorem will mention "quining".