It varies from University to university, course to course.
Both Aberystwyth and Nottingham have invited me to Visit Days, in the next week or so (Aberystwyth has around 5 Visit Days to choose from). That's after they made me an offer.
Southampton invited me to a Visit Day before making me an offer, which had a "1on1 informal chat with academic staff", which was basicaly as it says on the tin. It was called an interview by everyone else who had been invited and by most other people on the day, but as soon as we got into the interview room, we were told it's really not lol. It had some interview-like questions, but it was pretty much a chat, a chance to get to know the applicant, and a chance for the applicant to ask questions.
The Visit Days are really useful, especially if you haven't been to an Open Day for the University. Southampton's included a quick tour of the department, got to see the labs and the gigantic computer room in the Zepler building. They took us on a coach tour of some of the accommodation, providing free lunch (sweet & sour and rice... awesome
), free sandwhiches etc for the afternoon, and a couple of presentations from members of staff on the department, its research and the applications procedure.
It's worth going to if you haven't been to an Open Day, and if they haven't made you an offer yet. I'm probably not going to Aberystwyth's because I spent 2 days there playing with robots in the Spring, and I went to Nottingham's Open Day and found time to view the accommodation etc.
On the other hand, my girlfriend got invited to a Visit Day by Bath, and simply emailed them asking if there would be anything different from the Open Day, and they replied saying it won't affect her application in the slightest by not attending (it's due to time, time out of school, money and so forth as well).