A Linux/UNIX configuration file (/etc/bashrc) that provides user-definitions to command aliases for that user's bash shell.

The bashrc simonc mentions at /etc/bashrc, by the way, is the global bashrc-- it applies to every user, whomsoever they may be. Each individual user, however, can have an individual, local bashrc at ~/.bashrc
Both of these files are run as scripts by the bash shell when the user logs in-- first the global script, then the user's local script. As simonc noted, usually the only thing in the bashrc files are alias commands, and commands setting up the appearance of the the prompt ($PS1).

Bashrc is not to be confused with bash_profile-- the difference is that bashrc runs every time you "become" that user by any means (including su), whereas bash_profile does not. bash_profile is run only when the user logs in proper.