BankID is by many associated with otp generator. That is, a way to log in by generate a OTP and entering a password. BankID on mobile is an alternative way of achieving exactly the same as BankID, by automatically picking up your mobile phone instead of making a one-time code with otp generator or other. Note that even if you have a BankID, you do not automatically have a BankID on mobile.
To get BankID on mobile, you must first have a BankID from a Norwegian bank, and you must also have a phone and a SIM card that supports BankID on mobile. If you have, you can log in to your online bank and order BankID on mobile. To check if your phone supports BankID on mobile, you can go here and test your mobile phone by typing your phone number: https://www.bankid.no/Hjelp-og-nyttige-verktoy/Nyttige-verktoy/Test-din-mobil/
This is the first image using regular BankID with otp generator. Note that a user must complete his or her full SSN.
BankID on mobile looks like this: phone number and date of birth are entered: