When you rent a property, you're usually responsible for paying council tax directly to your local council. This is separate from your rent. The amount varies depending on where you live, the council tax band the property falls into (based on its value in 1991), and whether any discounts or exemptions apply to you.
If you live alone, you're entitled to a 25% single person discount, and full-time students are exempt from council tax entirely. If you receive certain benefits, you may be eligible for council tax reduction (also called council tax support), which can reduce or eliminate your bill.
It's important to register for council tax when you move into a new property and to cancel it when you move out, giving the exact dates. If you don't, you may be charged for a period when you weren't living there. Your landlord shouldn't be paying council tax on a property that you occupy, and if council tax is included in your rent, check the terms carefully.