@Tomislav - Although heel pain is not as serious as chest pain, I would still go see a doctor about it (and I used that metaphor of chest pain because I would surely hope you would go to the doctor if you had chest pain while walking)!
I just found out from my orthopedist that the pain in my heel I felt when walking was due to plantar fascitis. And just like the pain you described it would often be at its worse after I sat!
Just as the article described it was due to an inflamed tissue, in this case the tissue is actually called the plantar fascia and it is right in the middle of the fleshy heel pad.
My orthopedist thinks part of the reason my heel is unhappy with me is because of my soccer cleats. He said they were notorious for not providing your foot enough support.