You can implement a compiler in any language, including the same language it compiles, a process called “self-hosting”.
You can’t compile it using itself yet, but if you have another compiler for your language written in some other language, you use that one to compile your compiler once.
Now you can use the compiled version of your own compiler to compile future versions of itself and you can discard the original one compiled from the other compiler.
This is called “bootstrapping” from the image of pulling yourself up by your own bootstraps.
A parser takes the flat sequence of tokens and builds a tree structure that mirrors the nested nature of the grammar.
These trees have a couple of different names — “parse tree” or “abstract syntax tree” — depending on how close to the bare syntactic structure of the source language they are.
In practice, language hackers usually call them “syntax trees”, “ASTs”, or often just “trees”.
