There are two passwords. If you forgot the password ***** login to Facebook application or Facebook website, then go to this website and follow the onscreen instructions to reset your password *****> https://www.facebook.com/login/identify
After resetting the password, use the new password ***** login to Facebook on your iPhone.
If you forgot the password ***** download Facebook application, then it is the Apple ID password ***** forgot.
If you don't remember the password, then you have to reset the password. You can reset it from here (go to this website from your computer) --> https://iforgot.apple.com/
Go to the above website. Use the "Get an Email" method to reset the Apple ID. Apple will send the reset instructions to the recovery email you setup with your Apple ID. It would be your email registered with Apple, like Gmail, Yahoo etc. Open your email and you will see the email from Apple. Open it and follow the instructions to reset the password.
If that didn't work, then go to this site again --> https://iforgot.apple.com/
This time use the "Answer Security Questions" and answer the security questions there to reset your password.Then use this password ***** download Facebook.
Please let me know if that didn't work, so I will continue to help you