You've been able to view Instagram profiles on the web for a while now but today Instagram has announced that you'll now be able to browse your Instagram feed to see all the photos people you follow are publishing, including the ability to like and comment on them just like on mobile devices.
"We believe that you should be able to access Instagram on a variety of different devices, any of which may be convenient to you at a given moment – including your desktop computer or tablet. We do not offer the ability to upload from the web as Instagram is about producing photos on the go, in the real world, in realtime. On the other hand, Instagram for the web is focused on making the browsing experience a fast, simple and enjoyable one."
Source: Instagram Blog