Modding allows things that are not in Starbound (like inventory editors) to be in Starbound. Modding allows for the changing of different elements found within the game. Mods can change the way your game looks (Texture Packs) the way you play the game (ex. Adventure/building) or a whole new side mission (Similar to DLC) Mods are free and easy to download.
It has been announced that Starbound will include a modding API, allowing for people to easily modify the game; it has been notioned that this feature will be available on launch with limited features but will be added upon later into development.
There are any theories on how Chucklefish will handle mod downloads (Particularly for servers); one of the popular ideas is that the server will autodownload the mods unto the client to play. Although no actual details on this have been given, several staff replies to threads on the forums hint at a possible system such as this.