If you live with one other adult who is not a full-time student, the property you are in will likely be charged for Council Tax. You might be able to get the rate reduced by 25% by informing your Local Authority that you (as an individual) are exempt. If you live with more than one non full-time student, however, then the property will be liable for the full Council Tax charge.
Your student status means that you are not legally liable to pay Council Tax, but if you live with non-students then they might still expect you to contribute towards the bill. It is important to discuss this with potential flatmates before you commit to living together.