If service, that starts your Activity, is yours service, you can put some custom information (using Intent#putExtra for example) in Intent you use to start Activity from Service. 
In Activity you can use Activity#getIntent(), that returns the intent that started this activity.
If you started Activity from Service, that Intent will be the one you passed in Service#startActivity, and will have your custom information. Otherwise, that was not your Service, that started your Activity.  
That could look somehow like that, for example: 
//in Activity
public static final String EXTRA_STARTED_FROM_MY_SERVICE = "com.example.extra_started_from_sevice";
private boolean wasActivityStartedFromService() {
    Intent startingIntent = getIntent();
    //assuming you will use Intent#putExtra in your service when starting activity
    return startingIntent.getBooleanExtra(EXTRA_STARTED_FROM_MY_SERVICE, false);
}
//...
//in Service
    //...    
    Intent startingIntent = new Intent(this, MainActivity.class);
    startingIntent.putExtra(MainActivity.EXTRA_STARTED_FROM_MY_SERVICE, true);
    startActivity(startingIntent);