How can a compiler compile itself?

The first edition of a compiler can’t be machine-generated from a programming language specific to it; your confusion is understandable. A later version of the compiler with more language features (with source rewritten in the first version of the new language) could be built by the first compiler. That version could then compile the next compiler, and so on. Here’s an example:

1. The first CoffeeScript compiler is written in Ruby, producing version 1 of CoffeeScript
2. The source code of the CS compiler is rewritten in CoffeeScript 1
3. The original CS compiler compiles the new code (written in CS 1) into version 2 of the compiler
4. Changes are made to the compiler source code to add new language features
5. The second CS compiler (the first one written in CS) compiles the revised new source code into version 3 of the compiler
6. Repeat steps 4 and 5 for each iteration

Note: I’m not sure exactly how CoffeeScript versions are numbered, that was just an example.

This process is usually called bootstrapping. Another example of a bootstrapping compiler is rustc, the compiler for the Rust language.