I try to do something for my partner every day. Cook a special meal, make her small treats, make her lunch and coffee ready for her when she gets out of bed, and I'm not sleeping, anyway.. I tell her I love her each and every day, and I try to tell her how special and important she is to me, too.
And she does, vice versa. I have to confess that, when she doesn't tell me for some time, I'll get a bit insecure. Even though I know better, it's not how I feel.. And at the end of the month, I just do need a little more attention than usual. I don't know; it's the time where I get cranky, head-aches, restlessness, tired.. I don't feel attractive, neither physical nor emotional. (Well; I never feel physically attractive, but hey..) I also feel it's terribly unfair; she doesn't get periods because she rarely takes breaks from the pill. I don't have woman-bits, and I get messed up each month.

So yes; loving her, being proud of her, adoring her.. It's really brilliant, but you have to tell her. Let her know. Even íf she knows; knowing isn't always enough. You want to hear it from their lips. Confirmed.
Trust me; you can never get enough 'I love you's, 'you're pretty's, and stuff like that.
Bút.. It has to feel heartfelt, too.
Demanding, much? I guess...
Edit: As for why do women want to hear it?
I think it's down to behavioural biology, really. There are, statistically, more women than men. Humans are, by nature, mostly monogamous. So when a woman gets a man, or partner, from a biological point of view, she needs to keep him/her/them. It's wired into the system. So if a partner shows they appreciate you, they ease the instinctive unease.
At least; that's what I've learnt in biology. I could be wrong, of course.