It's essentially a rating system. Tag #1 means you're really good. Tag #328 (my tag) means you just bought one a couple weeks ago, haven't played anyone for it, or I suck. All three are true. Does anyone have a tag number higher than mine? I'll play them for it. If I can't be first, I may as well be last.
You can buy them for $5 from Disc Golf World in KC. They have a bottle opener on them, so they're versatile.
Any time you play a round with someone else with a bag tag you're supposed to "wager" them. Low score on the round takes the lowest bag tag, highest the highest bag tag, and everyone else in between. The rules are likely on page 1.