1. To enter one's name on a website or software application. You'll need to register on our mobile app before you can start using our service. My wife registered on the website two years ago, but wasn't able to remember her password.

2. To enter someone's, something's, or one's own name and details on an official list or record. In this usage, a noun or pronoun is used between "register" and "on." I suggest registering each of your family members on the State Department's website before you travel. She registered the business on a database of recruiters to help find new employees.