I always liked the SF, so I'm not sure how to persuade anyone who hasn't. I think Use of Weapons is the best, but Against a Dark Background might be a better way in, perhaps...

And as to why: limitless resources, extended lifespans, body-mods and gender-swapping, a galaxy full of adventure and change... Who wouldn't? The Culture is all about learning what it means to be human when the drudge of work is gone and everything is mutable, accessible, on offer. It's a kind of socialist utopia, with very very sharp edges.