The bash prompt is created by setting a variable called PS1. You can see what your prompt is set to with:
How PS1 is set varies from one distribution to another. PS1 can be set universally in /etc/bashrc or /etc/profile. A user can set his own version of the bash prompt in /home/user/.bash_profile or /home/user/.bashrc.
Here is a complete explanation of the bash prompt including what all of the arcane symbols used in PS1 mean: