[Based on Android source code:]
At the C++ side, the SurfaceFlinger implements the captureScreen API.  This is exposed over the binder IPC interface, returning each time a new ashmem area that contains the raw pixels from the screen.  The actual screenshot is taken through OpenGL.
For the system C++ clients, the interface is exposed through the ScreenshotClient class, defined in <surfaceflinger_client/SurfaceComposerClient.h> for Android < 4.1; for Android > 4.1 use <gui/SurfaceComposerClient.h>
Before JB, to take a screenshot in a C++ program, this was enough:
ScreenshotClient ssc;
ssc.update();
With JB and multiple displays, it becomes slightly more complicated:
ssc.update(
    android::SurfaceComposerClient::getBuiltInDisplay(
        android::ISurfaceComposer::eDisplayIdMain));
Then you can access it:
do_something_with_raw_bits(ssc.getPixels(), ssc.getSize(), ...);
Using the Android source code, you can compile your own shared library to access that API, and then expose it through JNI to Java.  To create a screen shot form your app, the app has to have the READ_FRAME_BUFFER permission.
But even then, apparently you can create screen shots only from system applications, i.e. ones that are signed with the same key as the system.  (This part I still don't quite understand, since I'm not familiar enough with the Android Permissions system.)
Here is a piece of code, for JB 4.1 / 4.2:
#include <utils/RefBase.h>
#include <binder/IBinder.h>
#include <binder/MemoryHeapBase.h>
#include <gui/ISurfaceComposer.h>
#include <gui/SurfaceComposerClient.h>
static void do_save(const char *filename, const void *buf, size_t size) {
    int out = open(filename, O_RDWR|O_CREAT, 0666);
    int len = write(out, buf, size);
    printf("Wrote %d bytes to out.\n", len);
    close(out);
}
int main(int ac, char **av) {
    android::ScreenshotClient ssc;
    const void *pixels;
    size_t size;
    int buffer_index;
    if(ssc.update(
        android::SurfaceComposerClient::getBuiltInDisplay(
            android::ISurfaceComposer::eDisplayIdMain)) != NO_ERROR ){
        printf("Captured: w=%d, h=%d, format=%d\n");
        ssc.getWidth(), ssc.getHeight(), ssc.getFormat());
        size = ssc.getSize();
        do_save(av[1], pixels, size);
    }
    else
        printf(" screen shot client Captured Failed");
    return 0;
}