A Software Development Kit (SDK) is the toolbox of the software development world. But instead of tools like screwdrivers and pliers, SDKs contain libraries and APIs (Application Programming Interfaces) that make it easier to create applications for specific software and hardware.
Some SDKs are required for developing a platform-specific app. For example, developing Android apps in Java requires the Java Development Kit, iOS apps the iOS SDK, and for Universal Windows Platform the .NET Framework SDK.
All of this is done through the libraries included in each SDK. A library is essentially a piece of software that allows your application to communicate with the specific platform its running on.
Tools for debugging and creating visual elements are often included in SDKs, making it easy for developers to fix their applications or create text boxes and buttons. Often SDKs also include sample code so developers can quickly become familiar with the platform they're coding for.