Code inside MainActivity.java
mainActivityButton.setOnClickListener(new View.OnClickListener() {
   @Override
   public void onClick(View view) {
        Intent intent = new Intent(MainActivity.this, FirstActivity.class);
        intent.putExtra("Editext1", editText1.getText().toString());
        intent.putExtra("Editext2", editText2.getText().toString());
        startActivity(intent);
        }
    });
Code inside First Activity.java
firstActivityButton.setOnClickListener(new View.OnClickListener() {
    @Override
    public void onClick(View view) {
         Intent intent = new Intent(FirstActivity.this, SecondActivity.class);
         intent.putExtra("Editext2Data", getIntent().getStringExtra("Edittext2"););
         startActivity(intent);
            }
        });
Update:
As you want to directly access main activity data. you can use static variable to store edittext data and get that data any where (Not a good approach)
in main activity intialize it globally 
public static String editext2_data = "";
Save data inside it on button click
mainActivityButton.setOnClickListener(new View.OnClickListener() {
   @Override
   public void onClick(View view) {  
         editext2_data = editText2.getText().toString();
        //Intent intent = new Intent(MainActivity.this, FirstActivity.class);
        //intent.putExtra("Editext1", editText1.getText().toString());
        //intent.putExtra("Editext2", editText2.getText().toString());
        //startActivity(intent);
        }
    });
From Second Activity Access static variable of MainActivity as
String data = MainActivity.editext2_data;