Do we actually move on?

Do we actually move on? I have never fully understood what that phrase actually means. When someone you love passes away you're given 'sound advice' by people, "You should be strong; You should move on." Is being brave so important and is 'moving on' absolutely necessary.
I still think of Dada so much, even though it has been more than a year since his passing. When someone you love has been ill for long and you see them battling a disease, you keep playing those times over and over again thinking if there was something that you could have done to save them. And yes, there are times when it makes me cry hopelessly and that's because I loved and miss my Dad so much.
So what actually do people insinuate when they ask us to move on? Is it that we shouldn't think of them (the loved ones who have passed) anymore? Or should we put on a brave face and pretend that in fact death has not affected us as much?
Then again, as much as a cliche it is, we have to carry on with daily activities of life and 'pull ourselves together.' So is this another demand of the society we live in so as to not appear an emotional wreck?
Also, is there too soon a time to get back on your feet and 'move on'? I took a break and joined Santhosh in Munich just after two months of Dada's passing. And though I was still recovering from the loss, being with Santhosh and being in a different country helped me in a way that I cannot explain. You may be patronized for going on a vacation when your parent has just passed but everyone has a different way of dealing with loss.
Though death or loss doesn't sink in too soon, ultimately we do get on with things to do, simply because they have to be done. And if that's called 'moving on' maybe that's just the course life takes and we just manage to slip into it's pattern.