"understanding what a compiler/text editor/perlbrew all are and how they work together"

Compiler:

A piece of software that takes the code of a high(er) level programming language, and transforms it through various means to machine code (ie. typically assembly (see machine code)), which the CPU understands.

Text Editor:

A piece of software that allows you to type text into. Common ones for Unix(y) platforms include vi/vim, emacs (both of those stated have a significant learning curve to them), nano, an easy one to use. There are also a slew of them for the Unix user interface. On Windows, a text editor would be notepad.exe. Some consider Microsoft Word a text editor, but I don't; it adds a whole slew of things into your document without you realizing it, so it doesn't turn out to be text-only. Don't use this (or Wordpad) for writing Perl (or code in any language). Notepad++ is probably one I'd pick to use on Windows if vim wasn't available.

perlbrew:

A piece of software App::perlbrew (berrybrew for Windows) that allows you to install and manage several versions of the Perl programming language on your system, without interfering with a system-installed perl, if available.

It allows you to do things on specific instances of Perl, and if needed, blow away the instance and re-install it with no side effects. Although there are many features I'm not explaining, it allows you to install versions of Perl in your own user home directory, so it doesn't affect anything other users may decide to do.

Summary:

You write your code in a text editor (eg: script.pl has all of your Perl code), and then have perl execute it (eg: perl script.pl). Perl (or rather perl (the lower-case form is the name of the interpreter itself)), then interprets the code in the script file you wrote with the text editor, and then *compiles* it into machine-ready code behind the scenes. It then passes it off to the CPU, which processes your instructions.