1. 新建一个Android Studio项目。
2. 在main文件夹下，新建assets文件夹，得到app/src/main/assets。把需要拷贝的文件复制/粘贴到其中。
   我这里放了2个文件，01.jpg和02.jpg。

3. 在AndroidManifest.xml中，授予 写外部存储 的权限。
   在<application>外加入：

<uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />

4. 修改MainActivity.java文件。

package ai.nixie.copyassets;

/*

Copy all the files in assets folder to your smartphone

From: app/src/main/assets
To:   /sdcard/Android/data/packageName/files/

*/

import android.content.res.AssetManager;
import android.os.Bundle;
import android.support.v7.app.AppCompatActivity;
import android.util.Log;

import java.io.File;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;

public class MainActivity extends AppCompatActivity {

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        copyAssets();

    }

    private void copyAssets() {
        AssetManager assetManager = getAssets();
        String[] files = null;
        try {
            files = assetManager.list("");
        } catch (IOException e) {
            Log.e("tag", "Failed to get asset file list.", e);
        }
        if (files != null) for (String filename : files) {
            InputStream in = null;
            OutputStream out = null;
            try {
                in = assetManager.open(filename);
                File outFile = new File(getExternalFilesDir(null), filename);
                out = new FileOutputStream(outFile);
                copyFile(in, out);
            } catch(IOException e) {
                Log.e("tag", "Failed to copy asset file: " + filename, e);
            }
            finally {
                if (in != null) {
                    try {
                        in.close();
                    } catch (IOException e) {
                        // NOOP
                    }
                }
                if (out != null) {
                    try {
                        out.close();
                    } catch (IOException e) {
                        // NOOP
                    }
                }
            }
        }
    }
    private void copyFile(InputStream in, OutputStream out) throws IOException {
        byte[] buffer = new byte[1024];
        int read;
        while((read = in.read(buffer)) != -1){
            out.write(buffer, 0, read);
        }
    }
}

5. 验证。
   开命令行，adb shell进入手机，可以在/sdcard/Android/data/包名/files/目录中，找到我们要拷贝的文件。

6. 几个常用的目录

String sdcardPath = Environment.getExternalStorageDirectory().getAbsolutePath().toString();
Log.d(TAG, "getExternalStorageDirectory: " + sdcardPath);
// getExternalStorageDirectory: /storage/emulated/0

String dataDir = getFilesDir().toString();
Log.d(TAG, "getFilesDir(): " + dataDir);
//getFilesDir(): /data/user/0/ai.nixie.copyassets/files

String externalFilesDir = getExternalFilesDir(null).toString();
Log.d(TAG, "getExternalFilesDir: " + externalFilesDir);
//getExternalFilesDir: /storage/emulated/0/Android/data/ai.nixie.copyassets/files


PackageManager packageManager = getPackageManager();
String str =getPackageName();
try {
    PackageInfo pi = packageManager.getPackageInfo(str, 0);
    str = pi.applicationInfo.dataDir;
} catch (PackageManager.NameNotFoundException e) {
    e.printStackTrace();
}
Log.d(TAG, "applicationInfo.dataDir: " + str);
//applicationInfo.dataDir: /data/user/0/ai.nixie.copyassets

Android Studio v2.3中测试通过。

References
https://stackoverflow.com/questions/4447477/how-to-copy-files-from-assets-folder-to-sdcard