You'll also get answers from posters working in universities in the Academics' Corner over in the work topic. My sense as an academic is that the bog standard admin jobs are little different from bog standard office administration jobs anywhere. Except you'll be supporting very driven and dedicated academic colleagues, and you'll often be expected to be driven and dedicated as well.
I work with some fabulous admin support colleagues who understand and are committed to the core activities of the university - teaching and research. If you're not prepared for that, look elsewhere, please!! We all work too hard to have someone who's not supportive of our core activities and values.
The conditions are usually pretty good, pension scheme good, pay about the same as other office jobs, although mostly, job security can be better, but NOT ALWAYS. But universities are very driven places, and do most amazing stuff on the smell of an oily rag ie scarce resource.
Universities are not the havens from neo-liberal crap most people think they are.
If you have a set of specialised skills, then you'll find progression into very interesting work - research project support, or internationalisation, or curriculum development. And so on.
But the top admins I work with are like most academics - they work over and above what they're paid to do.
I'm lucky - our Departmental administrator is fantastic. They understand what we do. They like working with the students and they are a central person in our team. Paid shit, though.