(continues...)
Women once understood that they are physically weaker than men, and it has consequences even seven or eight millenniums afterwards. Women (though they will never admit it) see the world as "violent", contrary to men, who mainly find it "competitive". Now you understand why women, even teenagers, look for company to walk with them in the streets, or look forward to living with a man by their side when they grow up. This makes them feel safe: the most important requirement to develop and fulfill their femininity. This doesn't mean that women depend on men to feel comfortable, protected, or free (believing that would be a terrible mistake); but they do prefer to count on the protection of a man to feel more comfortable.
When they find this security (observation: most women consider this thought a stereotype in the beginning but they actually accept it some minutes later), the next step in a woman's world is to take care of their immediate environment (including her man, if any). As women's brains works inwards>outwards, not only do they have to be beautiful, taking care of themselves... their immediate environment also needs to be beautiful. That is why women care so much about that "pretty little ornament" or that other "crazy little thing" would look great beside the "remember that beautiful flower pot we have got in the kitchen?" you bought the last time you two went out. This helps them to free their intimacy, another major part of their femininity.
Should there be a last thing to mention about women and their worlds is that women need to communicate often to feel connected. This means talking, looking, touching, going, returning... but essentially talking. You may need to consider if you are a good listener these days. That can really help you.
Just be careful not to make the same mistake every other man on earth makes. Ironic as it will sound, women talk just to be heard, not for you to solve whatever problem she is discussing. I repeat. Women do not want you to fix things, they want you to listen, be sympathetic and tell them about a time when you felt the exact same way. When men listen to a problem, they immediately think on doing something to solve it. Do not do that, just listen without offering advice or, if you feel you must do something, ask: "Is this one of those times when you want me to listen and not give you advice, or can I say something?" If you do it this way, she will see you really understand her and she is going to appreciate it (and you) a lot.