For starters, it says it says he is the director for Medical Aid for Palestinians. That's a big clue. I'm 95% sure the "besieged services" have to do with medical aid. That would mean ambulances, hospital emergency rooms and things like that.
He means it quite literally. Gaza is quite literally being besieged as I write this. That means that medical supplies from the outside have been cut off, and worse—medical facilities are being bombarded from across the border.