The Youzify media gallery is enabled automatically with the Youzify plugin. This gallery looks like this:

The media files are added to this gallery automatically from the user's uploads to the activity posts:

All the media files uploaded to the activity posts will be added to the Youzify media tab automatically.
However, take into account that the Youzify gallery doesn't provide a possibility to upload media files directly on this page, unlike the rtMedia gallery. This gallery shows only the uploads from the activity posts.
On the Olympus demo, you may have seen the Media gallery on the user's profile page, which looks like this:
This gallery is provided by the rtMedia plugin. The plugin integrates with BuddyPress to allow your users to upload media files directly to the gallery with the "upload" button. All the possibilities of the rtMedia gallery you can find in its official documentation.
The rtMedia was the main Olympus gallery until Youzify added similar media functionality to their plugin. Now it is optional. If you want to create the same gallery on your site, you need to install and set up rtMedia additionally.
Since this plugin is free, you can find it under Plugins > Add new and install there:
If you installed the rtMedia gallery on your site, you will have two different media galleries. The first is for rtMedia uploads, and the second is for Youzify attachments. These media files can't be united into one gallery.