Which HP model, specifically, do you have? Here is a list - http://support.apple.com/kb/HT3669#HP - of the currently Apple supported HP printers and from here - http://support.apple.com/kb/DL907 - you can download the latest drivers.
It could really be anything - your printer isn't supported under OS X, you don't have the correct driver, you haven't set up the printer properly, etc.
Take a look and see if your printer is on the supported list. If it is, try downloading the latest drivers and removing and reinstalling the printer.