Hi, I need help because I don't understand how the pass works.I am living in Germany and would like to go to Edinburgh in June. My question is the following, once I buy the 4 days in 1 month pass, should I buy the tickets for the trip to Edinburgh or do I just get on the trains?

If you don't take trains where you have to make a reservation, you can travel to Edinburgh with your pass.

The only way to go by train to the UK is by using the Eurostar and for that train you need to have a reservation. That reservation will cost extra and you should make the reservation as soon as you know what date you will travel as the seats might be sold out.

Yes, Eurostar reservation is 30 euros in 2nd class and 38 euros in 1st class.

Check on the interrail app if your train journey requires a reservation, then book reservations through the interrail portal. Some high speed intercity trains require reservations. Trains that do not require a seat reservation you just board and go - remember to enter the journey details on your paper pass or into the mobile pass app.  

London Kings Cross to Edinburgh timetable and (free)  seat reservations.

You can book reservations anywhere you like; there is no obligation to book via Interrail.