“Senatus Populus Que Romanus” or The Senate and the People of Rome
SPQR was a publicity or propaganda campaign to promote the new, Republic of Rome. The campaign was to promote pride of the Government anytime someone saw the letters SPQR. You will see these letters all over Rome, on ancient buildings, on the sidewalks, on the ruins, sewer grates, etc.
For more information check out this cool site, games included: http://rome.mrdonn.org/SPQR.html
or this more boring but slightly more informational site: http://www.unrv.com/empire/the-senate.php