Finally Instagram has launched the profiles on the web ! Meaning ?
Now you can check your profile or others' online, see pictures, comment, give likes, edit your profile and also follow people. But you can't upload photos on the web. I believe this is better, otherwise a large number of people will forget about the app and start using the website, and by the time they are used to the website they will find it hard to open the laptop, upload their photo, tag it and then publish it. The beauty of Instagram app is that you just take a photo, upload it and end of story ;)
However, if you would like to see your profile and your photos in a bigger screen just go to www.instagram.com/YOURUSERNAME
This will help you to share your own profile with anyone you want to see your instagram photos. Also, it's an easy way for you to follow other users, find new users and meet new people. Better yet, people don't have to be instagram users to view your profile (if not set to private) which is by simply visiting your instagram profile on the web.
After all, this is a good step from Instagram :-)