A short, friendly way of saying university — you just cut the word down. It is very common in British and Australian English, and students use it constantly: at uni, go to uni, finish uni, uni friends, uni life. Notice that in these phrases it often takes no 'the', the same way we say at school and at work: "She's at uni in Leeds." Americans mostly do not say this; they say college for the same idea, and an American might not even recognise uni at first. It belongs to casual speech and messages between friends. In a job application, a scholarship essay, or anything official, write university. Saying it in an interview is not wrong exactly, but it sounds young and relaxed, which may not be the tone you want. (There is a completely different uni on menus — the Japanese word for sea urchin, the orange part you eat on sushi. Same spelling, different word entirely, and here we mean the university one.)