Display back button of action bar is not going back in Android

Add the following to your activity.You have to handle the click event of the back button.

@Override
 public boolean onOptionsItemSelected(MenuItem item) {
      switch (item.getItemId()){
         case android.R.id.home:
              onBackPressed();
              return true;
       }
   return super.onOptionsItemSelected(item);
 }

I would suggest not to handle "android.R.id.home" in onOptionsItemSelected as it is brittle. Rather you should override onSupportNavigateUp method.

@Override
 public boolean onOptionsItemSelected(MenuItem item) {
      switch (item.getItemId()){
         case android.R.id.home:
              onBackPressed();
              return true;
       }
   return super.onOptionsItemSelected(item);
 }

Note: If you are using onOptionsItemSelected , then you should return false as default otherwise onSupportNavigateUp method is not called.

Here you have 2 options:

a) provide a parentActivityName to your SecondActivity tag in AndroidManifest.xml like this:

 <activity
    ...
    android:name=".SecondActivity"
    android:parentActivityName=".MainActivity" >

b) override onOptionsItemSelected in SecondActivity like this:

@Override
public boolean onOptionsItemSelected(MenuItem item) {
    switch (item.getItemId()) {
    // Respond to the action bar's Up/Home button
    case android.R.id.home:
        onBackPressed();
        return true;
    }
    return super.onOptionsItemSelected(item);
}

I would suggest reading this guide for more information.