I assume that the alert allows you the option of pressing OK, Cancel or similar and that the system completes its startup process after you do so.
If that's true, then it is not serious. What is means is that you have downloaded an update for your printer from HP and that, for some reason, it is a corrupted download.
Since printer updates normally require a system reboot, the update routine put something in the startup process that is intended to complete the installation.
You can try and search for it by using as much of the name as you can get from the warning. If you find it, move it to the desktop. Moving it to the desktop, rather than trashing it, is a safety value incase it is tied to something else. Write down where you found it incase you need to put the file back.
AFter you find it and move the file, try and reboot to insure that the alert message is no longer present.
If so, go back to HP and see if there is an update for your printer. IF so, download it and go through the install process as if you've never attempted it before.