Instagram says that over 250M people use its Snapchat-like Stories every day, even more than the 200M that were reported back in March. But Stories so far were tied to the mobile apps and that limited their visibility to users. Now, Stories will start showing up on the mobile website as well. (The desktop site still doesn't have them.)
Starting today and over the next weeks, Stories will show up on the top of your feed when you visit instagram.com from your mobile browser. You can view any story by tapping it and switch by tapping the left and right arrows on the side of the screen.
But that's just viewing. If you wanted to post Stories from the mobile website, you will have to wait as the feature will roll in the next months.