Instagram is in the process of rolling out Instagram Profiles on the web. While there have been a number of services out there that allow you to view and share your Instagram profile online, this is the first official effort directly from Instagram. It isn’t clear what logic Instagram is using in timing their rollout to individuals. As of the time of this writing my Instagram profile on the web is not yet active but I’ve seen a number of users who’s profiles are already live. The logic doesn’t appear to be based on number of followers or even how long your account has existed. If your web profile isn’t yet active, not to worry, IG promises it will be live within the next few days. You can check your personal profile by visiting http://www.instagram.com/[your_user_name]. For example mine is located at http://www.instagram.com/appdaptation
The profile pages that I’ve seen look pretty attractive. Unfortunately your images themselves aren’t going to look that great at larger resolution because all your images are compressed when they get uploaded and stored on IG’s servers. Instagram web profiles do take into consideration your profile status so if your profile is set to public it is automatically viewable by anyone who knows your username. If your profile is set to private then only those people who you’ve approved can see your profile based on your current followers in the mobile app. Thus, if you do have a private profile then no one can see your Instagram profile on the web unless they are first signed in to Instagram (in their browser) and also have been approved by you to follow and access your IG profile.
For more information have a look at the official Instagram help page for web profiles.