Look in the MATLAB installation directory. You will see two or three .txt files there. In current releases license_agreement.txt is the file you need.
If you are like most universities, you will need to work with three of the license types listed there, with the Home license not applying to you.
You are going to be most immediately concerned about the Academic licenses as those discus what faculty and staff can do. If you happen to have a Total Academic Head Count campus license that permits student use then that falls under the Academic license terms.
If you do not have a Total Academic Head Count license then you will find yourself dealing with students about the licenses that are really their license and not yours. However, they will ask you to do things for them that you are not permitted to do under an Academic license, and they will not understand their licence and will assume that their problems are somehow the university's problems. You will find that in practice you will need to know the Student license terms as well to be able to advise the students.
Thirdly, Universities often have collaborations with business that are not strictly academic, including working with businesses that professors own or have major shares in as knowledge gets spun off. Chances are also high that parts of the university will engage in Fee For Service contracts, which can include businesses asking for a problem to be solved, and can include businesses paying for studies to be done. If the university does not end up owning all of the rights (including free rights of publication and all intellectual property rights) then chances are that Mathworks will say that such work is not strictly academic and so does not fall within the limits of Academic licensing. Therefore chances are good that there will be some Standard (also called Commercial, or Professional) licenses around. At the very least you will need to be familiar with the license terms to be able to tell faculty and staff when they cannot use the Academic license; it would also be common for you to be asked to act as license manager for some of those licences and perhaps run the licence servers too.
All of this is a different question than which licenses the university owns or manages. Or how to mediate arguments between groups complaining about other groups hogging licenses.