It is good to know as much as possible about them from them & from their peers & customers. Just giving them time to talk to you regularly about what is going on with them both in & out of the workplace will give you the visibility on how you can help them as well as build a relationship that is key to managing people well. Understanding what their goals are, what they enjoying doing, what their talents are & who they are as people can help you get them in the right role & to be successful. Soliciting feedback from people they work with will also fill in the gaps of what they may not know about themselves to help you understand their talents and challenges as well!
The Gallup Survey discussed in "First Break All The Rules" shares a Twelve Question (Q12) list to measuring employee engagement. Walking through these questions w/ your staff may bring up things you didn't know about them & spark great conversation.
Information you need to know about your employees is up to you. There are many questions that you may want to ask them while in the hiring process. Have they been convicted of a felony? Do they have the right amount of education to work for you company? What is their past work experience? These are just a few questions that are vitally important to knowing who you have working for you.
It just depends. If your employees do their jobs well, then that should probably be all that is necessary to know. If not, then you may have more questions, such as reasons their work is less than satisfactory. Perhaps they have mental health issues, a history of bad working relations, or some other personal issues.