A Spotify URI (Uniform Resource Indicator) is a link that you can find in the Share menu of any track, album, or Artist Profile on Spotify.
When you click a link that consists of a Spotify URI (rather than an HTTP address), you're taken directly to the Spotify application, without having to go through the web page first.
To find a Spotify URI for a track, album, or artist profile:
Go to the three dots
Go to the Share menu
Select 'Copy Spotify URI' from the second menu
You'll also see the options to copy Song Links and Embed Codes. To learn more about the different options for sharing songs, check out this article.
Note: If you're on the New Desktop Experience you'll see that the sharing options in the context menu have been reduced to Copy Link and Copy embed code. You can still copy Spotify URIs if you hold down the modifier key (Alt/Ctrl) in the share menu: