Here is a brief description of .apk and .dex extensions of Android:
.apk Extension: Android uses the .apk file extension for it applications. It denotes an Android Package (APK) file, a variant of the JAR format that is used for distributing and installing bundled components onto the Android operating system. In other words The extension for an Android package file, which typically contains all of the files related to a single Android application. The file itself is a compressed collection of an AndroidManifest.xml file, application code (.dex files), resource files, and other files. A project is compiled into a single .apk file.
.dex Extension: Android programs are compiled into .dex (Dalvik Executable) files, which are in turn zipped into a single .apk file on the device. .dex files can be created by automatically translating compiled applications written in the Java programming language.