In what manner could someone describe a character with regards to the things that are important to him/her? Associating characters with objects, through which they could be described and given depth. Do you think it's crucial to a story? Examples are more than welcome
You would tell by how the person interacts with the object. A man who displaqys a sword on an otherwise bare wall, and takes it down frequently to lovingly hone and oil the blade is likely a skilled swordsman who takes great pride in his skills. On the other hand, it may be a revered heirloom, and the care of the blade may be his way of honoring the person who wielded it.
Laura Wingfield in The Glass Menagerie is one of the best examples I can think of, off the top of my head. I don't know if it's crucial to a story, and if handled badly could actually be detrimental, but when skilfully done, it adds lovely layers.
I don't know that its ever crucial....the glass unicorn in The Glass Menagerie is a perfect example though...that one object and the things that happn to it are basically a metaphor for the character's whole life...Tennessee Williams uses those kinds of things quite often actually (the memory of Belle Reve in A Streetcar Named Desire fulfils almost the same function). It is the kind of thing that really depends on what you are writing though. For some characters, associating a particular object with them will allow you to bring out or reinforce aspects of their character, while for others it will just be tacky and unnecessary. If you have a great example already in mind, go with it, but I wouldn't force it if you can't come up with something that is really amazing.
I think little things about a person can build that character. Let's say he wears spiky bracelets and mascara. What about a guy who always carries his comb in his back pocket? He often runs in through his hair. What about a guy who takes a handheld gaming device with him when ever he leaves the house and plays it while he has to wait in lines, or has do wait anywhere for any reason. << That's me. That says a lot about me, right? A woman that has a portable makeup kit in her purse, and often checks her make-up. A guy that always wears a baseball cap. He's balding.
Is it critical to include such items? No. But it certainly adds depth to the inner workings of a character. I like idea of including a small personal item in every character's bio. Sometimes its expressed in the story and other times its not. Example: pictures work well. It tells a little back story without telling a back story.