Instagram (for Android): Main Feed
The home feed is probably where you'll spend most of your time, viewing, liking, and commenting on images. Note the addition of a Direct inbox in the upper right.
Instagram (for Android): Filters
The latest version of Instagram sports new controls for each filter, along with more powerful editing tools hidden in the wrench menu.
Instagram (for Android): Video Filters
Unsurprisingly, Instagram includes several video-only filters. Somewhat surprisingly, you can't film with the filters engaged.
Instagram (for Android): Share Page
Your Instagram creations are surprisingly mobile as the service lets you share images with a number of other social networks. You can also send any image or video Direct to another user.
Instagram (for Android): Instagram Direct
The newest feature in Instagram is Direct, which lets you send an image to other users without posting it publicly.
Instagram (for Android): Instagram Web
You can like and comment on images from Instagram's web interface. Uploading images of sleepy red pandas requires a mobile device.
Instagram (for Android): Video Editing
Instagram still struggles with video issues. On several devices I tested, it was not possible to focus the camera. The viewfinder on the Samsung Galaxy S4, seen here, is completely unusable.
Instagram (for Android): Following
The following section of the News tab is a great way to find new images and users. I think it's better than the Discover section.