This is the operating system, not Flash Player, prompting for your password, therefore, this is the password you use to log into your computer. If you're user is not an Admin you'll need to provide the user name and password for an Admin as Flash Player requires Admin permissions for installation. Please see What userid & password do I need to install Flash Player? for more information.
This password prompt is presented by your operating system, and is intended to keep you from accidentally installing software.
If this is your personal machine and you don't need a password to log into the computer when it first starts up, you can probably leave the password blank and click OK to get past this prompt. If this is your personal machine and your normal password isn't working, check to make sure that CAPS LOCK is off, and type the password carefully.
If this is your work machine and it's asking for an Administrator password, well, you'll need to have a conversation with your friendly IT person.
If you're still stumped, you may need to reset the password on your Mac: