H is just a booking fare. Generally airlines assign letter codes to their various fare classes. For example on Delta T and U are the cheapest fares. Once those are gone you move up to some other letters Y is full fare for example. F is first class...
The class will have rules associated with it. For example a DL Y is fully refundable, can be changed at any time etc and costs a fortune!!! A T fare is very restricted but costs less.
You might try the website for the specific H rules, but it's probably easier to call.