第一种：

通过公用的Handler 更新Activity

MyApplication 方法

public class MyAppliacation extends Application {

    private static MyAppliacation myAppliacation;
    public Handler handler =null;

    public Handler getHandler() {
        return handler;
    }

    public void setHandler(Handler handler) {
        this.handler = handler;
    }

    public static MyAppliacation getInstance(){
        if (myAppliacation==null){
            synchronized (MyAppliacation.class){
                if (myAppliacation==null){
                    myAppliacation = new MyAppliacation();
                }
            }
        }
        return myAppliacation;
    }

    @Override
    public void onCreate() {
        super.onCreate();
    }
}

MainActivity

public class MainActivity extends Activity {


    private Button MainButton;
    private TextView MainText;
    private Handler handler = new Handler(){
        @Override
        public void dispatchMessage(Message msg) {
            Log.v("abc--","Handler更新MainActivity界面");
            MainText.setText("通过handler更新数据");
        }
    } ;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        MainButton =findViewById(R.id.MainButton);
        MainText =findViewById(R.id.MainText);
        MainButton.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View view) {
                    MyAppliacation.getInstance().setHandler(handler);
                    Intent intent = new Intent(MainActivity.this,A.class);
                    startActivity(intent);
            }
        });


    }
}

public class A extends Activity {

    private Button AButton;
    @Override
    protected void onCreate(@Nullable Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.a);
        AButton = findViewById(R.id.AButton);

        AButton.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View view) {
                MyAppliacation.getInstance().getHandler().sendEmptyMessage(1);
                A.this.finish();
            }
        });
    }
}

运行结果：

07-19 13:17:12.617 2462-2462/com.example.activityhandler V/abc--: Handler更新MainActivity界面

第二种方法 通过广播的形式 BroadCastReceiver

BroadcastReceiver broadcastReceiver = new BroadcastReceiver() {
    @Override
    public void onReceive(Context context, Intent intent) {
        MainText.setText(intent.getExtras().getString("data"));
    }
};

 MainButton.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View view) {
//                    MyAppliacation.getInstance().setHandler(handler);
                    Intent intent = new Intent(MainActivity.this,A.class);
                    startActivity(intent);



            }
        });

public static final  String action ="jason.broadcast.action";

Intent intent = new Intent(action);
intent.putExtra("data", "BroadCast通知更新数据");
sendBroadcast(intent);
finish();