Vine announced the new higher-resolution videos in a blog post, adding that they will be viewable on their iOS and Android apps "over the coming days". Vine video posts made from the iPhone can already support the new 720p format, and videos with this new higher resolution can be viewed on the web. From Vine:

When you watch Vines on our iOS and Android apps, you'll see these quality improvements — they are rolling out over the coming days. You'll also see higher quality Vines embedded in sites across the web.

It doesn't appear that you need to download an app update to see the new 720p videos on the iPhone version of the app, though you should probably update the app to the latest version, 3.2.1. The most recent major update to Vine added offline viewing support.

Source: Vine