It depends on the department, but the publishing process is generally about seeing through a book’s production from start to finish, promoting the book/author and ensuring it’s available to sell. But this is a very, very simplified understanding of publishing and marketing/publishing doesn’t just start when a book is published and it doesn’t just apply to physical books - publishers might produce apps or interactive eBooks, for example.
There’s all sorts of different departments that work together: editorial, production, marketing, digital, design, digital sales, publicity, sales, export sales, rights, royalties and accounts, and more specific job titles within these departments like digital marketing executive or social media assistant, and many more.
I’m a marketing executive (so one step up from assistant) and I work closely with the publicity team to do tasks such as: manage the social media accounts and websites, manage the seasonal catalogue that’s produced every six months and used by the whole company, and help produce any sort of physical and/or digital marketing material such as bookmarks, adverts, banners, flyers, videos, tote bags, badges, online graphics. But like any role in publishing, it’s quite varied!
Publishers in the UK are mainly based in London and there’s definitely internships available during term-time. You’re probably more likely to get one at that time because everyone wants them during the university breaks.
(For others, I answered another question about getting into publishing here).