Twitter introduced two-factor authentication via SMS back in May, but it was next to useless for Australian customers, since it only worked with Telstra mobiles (and not always reliably for those). A new option that sends security verification messages directly to Twitter's native apps for Android and iOS sounds more promising.
Sending login verification messages directly to the Twitter apps means the option will work no matter what carrier you use. As Twitter's announcement points out, this is also useful if you manage multiple Twitter accounts.
As with SMS two-factor, this isn't perfect: if someone has access to your phone, they can authenticate and access your account. But it's certainly better than doing nothing.
You'll need the most recent version of the app for this to work; hit Twitter's blog post for details on how to set it up.
Improvements to login verification, photos and more [Twitter Blog]