A Software Development Kit (SDK) is a set of software development tools, that includes program codes, interfaces and instructions for developers. Using these SDKs, developers can create software that runs on certain operating systems, hardware, or in combination with other software.
In order to create suitable software for certain platforms or hardwares, hardware developers usually offer SDKs. In most cases the licenses are only handed out to professional developers, but sometimes they might as well be accessible for hobby developers.
Open source softwares like Open Office, Firefox or Footbar 2000 usually evolve as professional and hobby developers, using the corresponding SDK, create new designs, functions, AddOns and PlugIns and share them with all users.
Apparently, Software Development Kits are also used to create mobile applications. Many companies are now providing customers the opportunity to use mobile software development kits to build their own apps.