I have pain in my right hill every morning, which fades away during the day. What can this be?

Plantar fasciitis. Sounds like it could be plantar fasciitis, which typically is worse upon arising in the morning and can persist to varying degrees throughout the day. You can also have a heel spur and or arthritic degenerative changes. See your doc and get an x-ray for starters.
Doctor can evaluate. Heel pain can come from a mild injury, such as jumping off a fence. It can come from overuse, such as hiking 5 miles when one is not a hiker. There can be irritation/inflammation of the arch area of the foot, or at the achilles' tendon from the calf, both of which are connected to the heel. Sometimes there is a bony heel spur at the bottom. A primary care, orthopedic, or podiatry doctor can help.