What is onCreateOptionsMenu(Menu menu)

Menu is just the type of the parameter menu. For example you can have a String type for a variable named string, dog, etc. And in this case there's a Menu type for a parameter named menu.

You use onCreateOptionsMenu() to specify the options menu for an activity. In this method, you can inflate your menu resource (defined in XML) into the Menu provided in the callback.

For example:

@Override
public boolean onCreateOptionsMenu(Menu menu) {
    MenuInflater inflater = getMenuInflater();
    inflater.inflate(R.menu.game_menu, menu);
    return true;
}

Fore more information, visit this link.

As for this,

Within an instance method or a constructor, this is a reference to the current object — the object whose method or constructor is being called.

For example:

public void sendMessage() {
    Intent intent = new Intent(this, DisplayMessageActivity.class);
}

The constructor takes two parameters and a Context as its first parameter. this represents environment data and provides global information about an application environment.

For more information on the intent example you provided, check this out.

The intent of implementing this method is to populate de menu passed with the itens you define in the R.menu.game_menu layout file.

Java

@Override
public boolean onCreateOptionsMenu(Menu menu) {
    getMenuInflater().inflate(R.menu.game_menu, menu);
    return true;
}

Kotlin

override fun onCreateOptionsMenu(menu: Menu): Boolean {
    menuInflater.inflate(R.menu.game_menu, menu)
    return true
}

After inflating the menu with the itens you might want to add some action when they are selected:

Java

@Override
public boolean onOptionsItemSelected(MenuItem item) {
    switch (item.getItemId()) {
        case R.id.menu_item:
            // Action goes here
            return true;
        default:
            return super.onOptionsItemSelected(item);
    }
}

Kotlin

override fun onOptionsItemSelected(item: MenuItem): Boolean {
    return when (item.itemId) {
        R.id.menu_item -> {
            // Action goes here
            true
        }
        else -> super.onOptionsItemSelected(item)
    }
}