Streaming as in all of the content is from the web and streamed (not downloaded) to your TV. You can also download some of the content, or use add-ons that enable you to PVR shows.
Check out
Kodi | Open Source Home Theatre Software there is a wiki section to get started.
There are several versions of Kodi including the link you provided, most people tend to go with the original (
Downloads | Kodi) as the updates are done there first and any add-ons are tested against that rev, versus the various versions that people package together.
There is a lot that you can do with it and the add-ons are endless. Add-ons are apps that provide content, (see
SuperRepo.org » Worlds largest XBMC addons repository with 1,300 or
XBMC | Add-on Repository), although these are unofficial most work.
As mentioned before Kodi is a little bit on the techie side and can be a lot on the techie side depending on what you want to do. But to start out its real easy to just follow the wiki, basxically you download and install Kodi (which is the media center) and then install the addons (the content) and enable them. You can customize the interface with different skins depending on your tastes.
Almost forgot Kodi also deals with all your movies, pictures and music, so if you have a large collection on a drive somewhere you can connect to it and get fanart for your movies and covers for your music.