From the Instagram Blog:
In addition to the updates to Explore, we’ve added the ability to go back and edit captions on your posts. When you share a moment to Instagram, a typo shouldn’t get in the way. This has been one of the top requests that we’ve heard from the community, and we’re excited to finally bring it to you today. You’ll find a new “Edit” option in the menu beneath your image. Tap it to edit your caption.