References are an essential part of finding employment. (They are not always necessary for casual employment.) They are a way of a prospective employer establishing that an applicant can be trusted. A personal reference is a confidential statement by someone who knows you well to say that you are suitable for the job.
For a student, or recent graduate, the 'someone' will usually be a teacher. One of the duties of a personal tutor is indeed to supply a reference on behalf of the University as to the character and general suitability of a student: to act as a referee for that student. When an applicant is asked for more than one reference or referee, as is common with graduate level appointments, it is common to ask a subject teacher who can vouch for the specialist knowledge or skills involved in the work. Later on in a career, applicants will usually ask the current, or a previous, employer to act as a referee.
It is polite to ask everyone you are going to name as referees before you add their names to the application that you are writing. It is also practical: a potential referee may be able to say "I am going on leave, and will not be available after Sunday. I advise you to ask someone else." People who are aware that they may be asked for a reference are also ready when the request comes to supply a considered response. When you ask someone to act as referee, tell them what post(s) you are applying for.
Be aware that some University (and other) information may use the word referencing to mean academic referencing.