Just found that unfinished manual, but it's really unfineshed. Right on the climax. I still don't get it.
Eshell is a command interpreter like a normal shell, but it does not run bash or any other shell underneath. Like bash, it has several types of commands: while bash has aliases, functions, and falls back to $PATH, eshell has aliases, lisp functions, eshell functions, and falls back to $PATH.
So, for example, you can run:
~ $ find-file foo.txt
and the lisp function find-file will be executed non-interactively (unlike M-x), meaning all necessary arguments must be passed in. This is one way to tell emacs to edit a file from eshell. It's probably faster to run C-x C-f, since it will default to the directory that eshell is currently in.
When you run:
~ $ ls
it actually runs the function eshell/ls, which will get a directory listing without calling /bin/ls. There are similar builtins; if you run C-h f eshell/ <TAB> you can get a list of them.
One of the major points of the eshell builtin functions is to make commands fit into other existing emacs functions. For example, grep will go into the *grep* buffer so that you can quickly jump to the results.
It also has aliases, which are somewhat similar to bash aliases, but act a bit like functions in the way they handle arguments. For example, in bash, you might say
alias ll='ls -l'
while in eshell you would say
alias ll ls -l '$*'
and both of those mean the same thing. The $* means basically "expand all arguments", and it's necessary to quote it. You can run alias to see all aliases you've created.