Selecting Open Details on the Web, opens up the design in your internet browser.
In the top left hand corner you will see the familiar A360 logo and next to it will be the file path to where the design is that you are examining. Next to the name of the design you will notice a little button with V3 displayed. Next to that is a drop down arrow. If you select the dropdown you will see the different versions that were created when you saved the design in Fusion 360.
Next to the different version numbers will be a thumbnail that shows what was changed (if there are any visual changes). It will also state who saved the design at each version as well as a description of what was done. If you did not put in a description when saving then there will be nothing in the description.
If you hover your cursor over each version it will give you an option to either view the Version or Promote the version.
If you view the version it will show you the model in your browser.
If you promote the design then you will be given the option to make that version the latest version.
You will also notice that the version next to the name has been bumped up to V4.