When I was a kid, I cried if I didn't get what I wanted. I cried when I lost something I liked a lot. When I was a teen, I cried when I lost the love of my life. I cried when I felt an utter loss of control over my life.
As an adult, you know what, I can honestly say I am quite similar. I lose something dear to me, I may cry. It's particularly bad when it's someone close to me--even if it's just them going away for a while. Add death to that, and...well...the finality of the loss in death is horrifying. Even if you believe in an afterlife, you're looking at perhaps YEARS without ever seeing the person again and even then you have no idea in what form you'll see them. I think, if there ever was a reason to cry, it's to cry over the loss of a loved one
I also find that I can be deeply moved by the prospect of others' sorrow. I see others going through a horrible time struggling with the loss and it tears me up inside too. Sometimes, then, I cry over a death not because I've lost someone, but because I know other people's lives have been thrown into shambles.
Does it have a literal, practical, application? Perhaps not (one may argue inter-personal connection, stress relief, etc as some have here). But most other emotions are pretty worthless on a totally practical level too. Love makes you do such stupid things, one could argue love is actually counter-productive and to be avoided entirely.
Incidentally, people talk about "this culture" as somehow emphasizing mourning. We emphasize mourning over tragedy here in America moreso than many other cultures (I can't stand how, sometimes decades after an event we're still mourning and commemorating it). However, many other cultures have much more elaborate and hysterical mourning processes after a person dies (screaming, bizarre rituals, hiring mourners, hysterics...). Interestingly, Americans often seem remarkably subdued at funerals by comparison
