Executing the content of "/etc/bashrc" sets the prompt variables. It's a shell script, just read it for more details. Te variables of interest in your case are named PS1, PS2, ... and PROMPT_COMMAND. See the bash manpage for the meaning of these.
Also, look in your "~/.bashrc", it's executed after "/etc/bashrc", so settins in ~/.bashrc are the last valid. In short:
1) after login, bash executes "/etc/bashrc" and sets PS1,PS2 ... to something
2) then in "~/.bashrc" they are set to something else or maybe unsets them
3) You "source /etc/bashrc" which brings you to point 1)