In these Google-powered beta groups, you gain access to early release versions of the application, and can then send in info to the developers, ultimately working to make the application better for everyone.
Joining is quite easy. Simply follow the link below, join the Google Group, then accept your spot as a tester right here on Google Play. Then, make sure to uninstall the current version of Instagram on your device and download the newest beta version from the Play store.
If you come across bugs, throw them into the Google Group and let the devs handle it.