If you give login a valid username and password combination, it will check in /etc/passwd to see which shell to give you. In most cases on a Linux system this will be bash. It is bash's job to read your commands and see that they are acted on. It is simultaneously a user interface, and a programming language interpreter.
As a user interface it reads your commands, and executes them itself if they are ``internal'' commands like cd, or finds and executes a program if they are ``external'' commands like cp or startx. It also does groovy stuff like keeping a command history, and completing filenames.
We have already seen bash in action as a programming language interpreter. The scripts that init runs to start the system up are usually shell scripts, and are executed by bash. Having a proper programming language, along with the usual system utilities available at the command line makes a very powerful combination, if you know what you are doing. For example (smug mode on) I needed to apply a whole stack of ``patches'' to a directory of source code the other day. I was able to do this with the following single command:
for f in /home/greg/sh-utils-1.16*.patch; do patch -p0 < $f; done;
This looks at all the files in my home directory whose names start with sh-utils-1.16 and end with .patch. It then takes each of these in turn, and sets the variable f to it and executes the commands between do and done. In this case there were 11 patch files, but there could just as easily have been 3000.
The file /etc/profile controls the system-wide behaviour of bash. What you put in here will affect everybody who uses bash on your system. It will do things like add directories to the PATH, set your MAIL directory variable.
The default behaviour of the keyboard often leaves a lot to be desired. It is actually readline that handles this. Readline is a separate package that handles command line interfaces, providing the command history and filename completion, as well as some advanced line editing features. It is compiled into bash. By default, readline is configured using the file .inputrc in your home directory. The bash variable INPUTRC can be used to override this for bash. For example in Red Hat 6, INPUTRC is set to /etc/inputrc in /etc/profile. This means that backspace, delete, home and end keys work nicely for everyone.
Once bash has read the system-wide configuration file, it looks for your personal configuration file. It checks in your home directory for .bash_profile, .bash_login and .profile. It runs the first one of these it finds. If you want to change the way bash behaves for you, without changing the way it works for others, do it here. For example, many applications use environment variables to control how they work. I have the variable EDITOR set to vi so that I can use vi in Midnight Commander (an excellent console based file manager) instead of its editor.
The basics of bash are easy to learn. But don't stop there: there is an incredible depth to it. Get into the habit of looking for better ways to do things.
Read shell scripts, look up stuff you don't understand.