SMAPI is an open-source modding API for Stardew Valley that lets you play the game with mods. It's safely installed alongside the game's executable, and doesn't change any of your game files. It serves eight main purposes:
Load mods into the game.
SMAPI loads mods when the game is starting up so they can interact with it. (Code mods aren't possible without SMAPI to load them.)
Provide APIs and events for mods.
SMAPI provides APIs and events which let mods interact with the game in ways they otherwise couldn't.
Rewrite mods for crossplatform compatibility.
SMAPI rewrites mods' compiled code before loading them so they work on Linux/Mac/Windows without the mods needing to handle differences between the Linux/Mac and Windows versions of the game.
Rewrite mods to update them.
SMAPI detects when a mod accesses part of the game that changed in a game update which affects many mods, and rewrites the mod so it's compatible.
SMAPI intercepts errors that happen in the game, displays the error details in the console window, and in most cases automatically recovers the game. This prevents mods from accidentally crashing the game, and makes it possible to troubleshoot errors in the game itself that would otherwise show a generic 'program has stopped working' type of message.
Provide update checks.
SMAPI automatically checks for new versions of your installed mods, and notifies you when any are available.
Provide compatibility checks.
SMAPI automatically detects outdated or broken code in mods, and safely disables them before they cause problems.
Back up your save files.
SMAPI automatically creates a daily backup of your saves and keeps ten backups, in case something goes wrong. (Via the bundled SaveBackup mod.)
Have questions? Come chat on Discord with SMAPI developers and other modders!