As Nonak said, it's downloading custom content that's made by the playerbase instead of an official update. It allows people to create what they want for their game (though it takes a lot of skill and time), and share their work for others to also use.
Stardew's a pretty big game so the modding scene is really diverse, and ranges from new areas, items, npcs to different mechanics (which might make some part of the game easier or harder depending on what you want), or which just change how everything looks to suit your tastes
Modding is unfortunately only possible on the PC versions and kind of limited on android