This week's book giveaway is in the General Computing forum. We're giving away four copies of Arduino in Action and have Martin Evans, Joshua Noble, and Jordan Hochenbaum on-line! See this thread for details.
The NDK provides access to a small set of native libraries (http://developer.android.com/tools/sdk/ndk/index.html#Tools), like OpenGL. And it has provisions for letting you implement methods in C/C++, going so far as making it possible to implement the entire lifecycle of an Activity in native code if you need to. It does not make available all the Java libraries to C code.
A few months ago, I wrote about the Android NDK for Apress's "Android Recipes, Second Edition" book, which is being promoted on JavaRanch this week.
My NDK chapter (which also covers Renderscript) discusses NDK installation, explores the various tools that the NDK makes available, itemizes NDK examples that are part of the NDK, and provides sample programs. The first sample, NDKGreetings, presents the Java and C sides of what I'd call a hybrid app. The Java side loads a native NDKGreetings library and proceeds to invoke its getGreetingMessage() native method in the app activity's onCreate() method. The C side uses JNI to return a message from the native equivalent of getGreetingMessage(). Moving forward from this simple JNI demo, I present low-level and high-level native activities in the C language. I show how to create and run all of these examples in command-line and Eclipse IDE contexts. I believe this chapter (8) will answer your questions for you.