The ILS stands for Integrated Library System. This means a system, which is comprised of the features and functionalities a library requires. It is just like an Enterprise Resource Planning solution specifically developed for library industry:

Administrative management
Acquisition of books and periodicals
Cataloging
Maintaining profile of patrons (staff, alumni, faculty, institutional members and so on)
Searching

In addition, an ILS is often comprised of a relational database, software to act on that database and two graphical user interfaces one is for intranet and another for OPAC (Online Public Access Catalogue)