You use your mastodon account to tell your mastodon instance to follow a user on the pixelfed.social instance. Your mastodon instance starts getting a feed of all the posts by that user from the pixelfed.social instance and displaying them to you in your mastodon timeline as if they were mastodon posts.
This works because while pixelfed and mastodon and tube.jenna.net display things differently, the things they are displaying are in fact very very similar. Posts by users, consisting of maybe a video, maybe an image, maybe a reference to a post they're replying to, and some text. Ultimately it will be up to the individual implementation what to do with posts that are different enough that they can't figure out a reasonable way to display them.