Briefly, LaTeX consists of several layers. (Those who were actually involved in LaTeX's development, please feel free to correct me.)
The lowest layer is the three hundred or so TeX primitives such as \hbox or \vskip.
On top of this, there is the LaTeX kernel. This is a set of macros such as \documentclass, \usepackage, or \begin. The source of the kernel is documented in the source2e document.
Each document written in LaTeX begins (more or less) with \documentclass{foo} which loads the file foo.cls, for example article.cls or book.cls. This file is another set of macros, this time written using a combination of TeX primitives and macros from the LaTeX kernel. These class files can also load another class to extend it or modify the macros from that class. It can also load packages which are up next.
LaTeX packages—that is, files ending in .sty (and their related files)—are additional sets of macros written using any combination of macros from lower levels. Some are specific to particular document classes, others are more general. These packages can be loaded using \usepackage from user documents, or \RequirePackage from classes and other packages.
At the highest level, the users' documents use a class file and optionally packages. As I'm sure you're aware, these documents contain macros written using any combination of TeX primitives and class- and package-defined macros as well as the prose, verse, and mathematics to be typeset.
There is a lot more detail that one could go into regarding things like fonts and class and package options, but this isn't so "brief" after all.
One final point, Knuth wrote TeX as well as the plain TeX macro package—a set of about 600 macros that make typesetting far easier than using just TeX's primitives. LaTeX was originally written by Leslie Lamport. LaTeX 2e—the most recent version—was also written by Johannes Braams, David Carlisle, Alan Jeffrey, Frank Mittelbach, Chris Rowley, and Rainer Schöpf.