Photo Sphere is one of the new features that comes with Android 4.2 Jelly Bean, and since only a small number of handsets have Android 4.2, only a handful of users can experience the Street View-like photos that come with it, and it's limited to only Google services as far as sharing goes. However, Google just enabled Photo Sphere embeds that allow web developers to insert a Photo Sphere onto any website.
You can check out an example of a Photo Sphere embed here, and Google details the process of adding a Photo Sphere to your website on their developer support page. The embed will allow you to click and drag around the photo to see a 360-degree view of the subject, as well as having the option of viewing the flat version as well.
Photo Sphere is one of the more popular features in Android 4.2 Jelly Bean, and it lets you take panorama photos that you can then view in a sphere-like manner, rather than just looking at it at a flat perspective like most panorama apps feature. Microsoft's Photosynth app is the closest that comes to Photo Sphere, but even that has its limitations.