This largely depends on the provider you go with and the policy you take up. However, some rules that are often associated with black box policies include:
A driving curfew, meaning you cannot drive between certain times (for example, during rush hour or at night time).
A mileage limit, meaning that you will be limited to a certain number of miles per month or per year.
Be aware, if you decide to have a black box installed in your car you might not have to adhere to rules like the above. This is wholly based on the black box insurance policy you choose to take out; some will have rules like the above, but many will not.