Why does iPods need password when installing an app
It always needs a Password for all Installs to protect you, or in case of App Store to identify you and your account.

You could change that settings but I would not advice that.

If it is your Apple ID then you can recover the password using the 

https://iforgot.apple.com/password/verify/appleid

It will send you a email to the account you used allowing you to reset the password or you can answer the questions to which you provided the answer when registering.