To an indoor cat, windows must seem strange. There's a whole other world out there that they are seldom allowed out in -- they only get out when they have to go to the vet, or when they slip out through the open door if we aren't vigilant enough. So it must seem so strange to them to see the squirrels and birds and rabbits and other cats, and to smell the outside air, and maybe not really understand it.
It's turned into Spring here, and we have the windows open as often as possible. And if the windows are open, the cats are sitting in front of them, night and day. In the daytime, there's the added benefit of a shaft of sunlight to stretch in.