Why? What made it different? Aside from tactically dominating the immediate environment, they obviously served as a last refuge and holdout against an invasion that might otherwise sweep around the castle and conquer everything else within a twenty mile radius. A castle that hadn't surrendered yet in this regard acts as a constant nuisance and thorn in the side of any offensive campaign that will try to subjugate everything quickly. With the hope of a relief force, the troops within the castle could then ride out and reverse the territorial losses easily.
Thats what castles were for, now imagine a network of them, while your force might be besieging an castle, that gave time for troops in other areas and castles to regroup and join an defensive army capable or relieving the besieged caste. In Medieval times the last thing you wanted was to have your forces surrounded while besieging an enemy castle. It was a very interesting defensive system.
From all castles i visited ( limited but still) The ones that stroke me in awe were the Alhambra in Granada, The templar headquarters in Tomar Portugal (Convent of Christ)
Alhambra
Convent of christ
A note for the Wawel castle in Krakow wich i visited not long a ago, i would mention the Neuschwanstein Castle as well, but its from another era alltogether...
I cannot pass the chance to mention the castle of the Moors, in Sintra because its where i basicaly grew up as a teenager. We used to go there and hang out with some friends, with bottles of booze and beer and other stuff , Sintra is a very beautifull place, this medieval castle among them.
( there is plenty of other stuff arround, world heritage of UNESCO Pena Palace, Quinta da regaleira as well ect) Its a very interesting place, with mystical undertones due to the Sintra Mountains and its gardens, hiden palaces, and keeps, and monasteries etc, if i recall correctly the romans called these mountains the mountains of the Moon, or something like that)
This is the castle were we used to hang out at times, when was free to enter, now it is still free for people who have their Municipal ID Cards, we even were able to do Abseiling in one of its towers, it is still comon to see people doing that, in the castle, not only in its towers but on cliffs and small moutains in it and arround it. Its one of its perks to be mingled with the natural mountainous geography.