Multidex Support / Training For Android Developers

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Android application (APK) files contain executable bytecode files in the form of Dalvik Executable (DEX) files, which contain the compiled code used to run your app. The Dalvik Executable specification limits the total number of methods that can be referenced within a single DEX file to 65,536, including Android framework methods, library methods, and methods in your own code. Getting past this limit requires that you configure your app build process to generate more than one DEX file, known as . 
A multidex configuration, in Android development is the way to bypass the Dalvik Executable (DEX) limit of 65536 (64K) methods within a single DEX file, So you can build bigger and better apps that new environments like Android 5.0 (Android L) brings.

So Android Developer has published an article "Building Apps with Over 65K Methods" that guides developers through.

Multidex support prior to Android 5.0

Versions of the platform prior to Android 5.0 use the Dalvik runtime for executing app code. By default, Dalvik limits apps to a single classes.dex bytecode file per APK. In order to get around this limitation, you can use the multidex support library, which becomes part of the primary DEX file of your app and then manages access to the additional DEX files and the code they contain.

Multidex support for Android 5.0 and higher

Android 5.0 and higher uses a runtime called ART which natively supports loading multiple dex files from application APK files. ART performs pre-compilation at application install time which scans for classes(..N).dex files and compiles them into a single .oat file for execution by the Android device. For more information on the Android 5.0 runtime, see Introducing ART.