I think there is a name for it: hoarding. Its sometimes classified as a psychological disorder that involves a person acquiring things and unwilling to discard them even though these things clutter the said person's life. Although your grandma's case cannot be classified as such because her things have no negative effect on her life.
Sometimes people don't want to let things go because they have sentimental value to them. It might present a certain memory they cherish.
Sometimes, people just don't want to throw away things when they are still useful.
Whatever the case may be, in my opinion, if it doesn't affect your life negatively its fine--keep your old stuff. But remember you cant let new things in when you'ree holding on to old things...