It varies by society, but at a basic level they're clubs you can join to meet people that you share interests with. Some of them may be academic based, some may focus on campaigning, some may compete (e.g. sport) or perform (e.g. music/drama), and some may just be general hobby-based groups.
To give some examples of societies at my uni and the sort of events they run:
Society A (academic): Coffee socials, revision sessions, drop-in sessions to ask for help with your modules, pub nights, barbecues, guest speakers.
Society B (social/campaigning): Weekly study socials, cafe meet-ups, picnics, welfare drop-ins, walks, campaigning with the SU, giving talks.
Society C (sport): Multiple practice sessions each week, competitions, gym sessions, nights out, meals, activity days, cafe meet-ups.
You can generally go to as many or as few events as you want/have time for, and pick and choose the ones that appeal to you. Societies are just a nice way to quickly find people you have something in common with, and have a shared activity/plenty of chances to get to know them.