Instagram, whom has traditionally only supported 640×640 pixel resolution, has began storing pictures at 1080×1080 pixels. While no official announcement has been made, you can view the source code of their website to see the new maximized resolution.
The higher resolution gives better quality photos but also provides a better means to print photos with online services. Not to mention, smartphones have increased screen sizes over the years and are able to display much higher resolution and at great quality, only being limited by the photo resolution.
While Instagram still has not given official word on the upgraded resolution we can expect that they will soon announce the higher resolution capabilities. In the meantime, you can get a sneak peak by browsing to an image page on the Instagram web site, view the source code and then do a “Find’ on the page for .jpg. The first .jpg found will be the link to the higher resolution image.