In the classic sense, an assessment center just means that it is an area that is devoted to conducting assessments. The location could be in an education department or HR area. These days, a lot of clinical assessment is online, so it may even be in a computer lab. Don't be surprised if you are asked to produce a picture ID and to leave your purse & electronic devices with a proctor. Cheating is pretty much rampant these days, so most organizations have procedures to minimize this possibility. it's not personal.
Relax, they'll provide you with all the information and instructions you'll need. Have fun with it. It's your chance to show off and let them know how good you are.