The term "swag" has some odd meanings these days. But when you talk about conventions, swag means the stuff you get to collect like a little autumn crazed squirrel as mementos, souvenirs and reminders of authors, artists and publishers you already like or want to know more about. I love this stuff and, yes, I'm a self-confessed swag hoarder.
The buttons, the bookmarks, the stress squishies, the odd and unique things, they come home with me and, for the most part, sit on my shelf. (Though things like pens and mint tins and occasionally lip balm, I actually use as well.)