the body of faculty and students at a university
"The entire university was buzzing with excitement after the professor announced her retirement."
establishment where a seat of higher learning is housed, including administrative and living quarters as well as facilities for research and teaching
"The sprawling university campus includes not only lecture halls but also extensive dormitories and state-of-the-art laboratories designed for advanced research."
a large and diverse institution of higher learning created to educate for life and for a profession and to grant degrees
"After earning his degree from the university, he was ready to apply his specialized training to become a practicing engineer."
Institution of higher education (typically accepting students from the age of about 17 or 18, depending on country, but in some exceptional cases able to take younger students) where subjects are studied and researched in depth and degrees are offered.
"After graduating high school, she enrolled at a university to study engineering and earn her degree."
In plain English: A university is a large school where older students go to study serious subjects and get degrees.
"She is studying biology at a local university."
Usage: Use "university" only for institutions that offer degree programs; do not use it as a generic term for any college or school of higher education. This noun is often confused with "college," so reserve it specifically for universities where research occurs alongside teaching at the undergraduate and graduate levels.
The word comes from the Medieval Latin universitas, which originally meant a group of people united into a single body or community. This term is derived from the Latin universus, meaning "whole" or "entire."