EA possibly feels bad about the continuing troubles of Battlefield 4, so they’re letting PC users have Battlefield 3 for free. It’s the latest game in the “On the House” promo scheme that EA has been running for the past few months. The previous titles given away for free were Dead Space and the original Plants vs Zombies.
Battlefield 3 is available for no money whatsoever until 3 June. At that point it won’t be free any more. That doesn’t mean it’ll disappear from your account or anything, though. If you make sure to get it before 3 June it’ll be yours forever (or until EA shuts down all the servers, or the internet explodes, or something.)
There isn’t really a catch to any of this (unless you consider needing an Origin account to be a catch,) so, er, hey, go get your copy of Battlefield 3. It’s just the Standard Edition so there’s no DLC, but it’s also completely free. Not a whole lot to complain about there.