As a general rule, maintenance covers all of your servicing costs, maintenance costs and replacement tyres (in some cases this even includes punctures). If your chosen contract is longer than 36 months in duration, the maintenance agreement would also cover your MOT costs to make sure that the vehicle is safe and road legal for you.
Just book your vehicle in with your local main dealer and let them know that has a full maintenance agreement. When the vehicle is serviced the invoice will be passed onto the leasing company for payment.