A lot of SWT tutorials show the creation of a Display, a Shell, and then a while loop to handle UI events and this leads a lot of developers to believe there is a 1:1 relationship between Display and Shell.
This is incorrect and although it works on Windows operating systems where the native SWT implementation supports multiple UI threads this approach does not work on GTK (Linux etc) based display managers. It is also bad practice as there is no need for multiple UI event dispatcher loops in your design.
In SWT a Shell represents a single window in the UI. You can have multiple Shells in the same application and this is classed as a Single Document Interface (SDI) design.
If you had a main container window which held multiple child windows that could not move outside their parent then this would be a Multiple Document Interface (MDI) design which is not supported natively by SWT but can be implemented easily using the excellent Novocode MDI library http://www.novocode.com by Stefan Zeigler.
Here is the code:
package com.chrisnewland.swt;

import org.eclipse.swt.SWT;
import org.eclipse.swt.events.SelectionEvent;
import org.eclipse.swt.events.SelectionListener;
import org.eclipse.swt.widgets.Button;
import org.eclipse.swt.widgets.Display;
import org.eclipse.swt.widgets.Event;
import org.eclipse.swt.widgets.Label;
import org.eclipse.swt.widgets.Listener;
import org.eclipse.swt.widgets.Shell;

public class SingleDisplayMultipleShells
{
  // ========================================
  // Inner class to represent a child Shell
  // ========================================
  private class ChildShell
  {
     public ChildShell(Display display)
     {
        System.out.println("Creating new child Shell");
       
        // =========================================
        // Create a Shell (window) from the Display
        // =========================================
        final Shell shell = new Shell(display, SWT.CLOSE);

        // =====================
        // Set the Window Title
        // =====================
        shell.setText("Child Shell");

        // ============================
        // Create a Label in the Shell
        // ============================
        Label label = new Label(shell, SWT.NONE);
        label.setText("Child");
        label.setBounds(0, 0, 100, 20);
        shell.setSize(200, 200);
        shell.open();

        // =============================================================
        // Register a listener for the Close event on the child Shell.
        // This disposes the child Shell
        // =============================================================
        shell.addListener(SWT.Close, new Listener()
        {
           @Override
           public void handleEvent(Event event)
           {
              System.out.println("Child Shell handling Close event, about to dispose this Shell");
              shell.dispose();
           }
        });
     }
  }

  public SingleDisplayMultipleShells()
  {
     // ======================================================
     // Create the main Display object that represents the UI
     // subsystem and contains the single UI handling thread
     // ======================================================
     final Display display = Display.getDefault();

     // ====================================================
     // create a shell for the main window from the Display
     // ====================================================
     final Shell mainWindowShell = new Shell(display, SWT.CLOSE);

     // =====================
     // Set the Window Title
     // =====================
     mainWindowShell.setText("Main Shell");

     // =========================================
     // Create a button that spawns child Shells
     // =========================================
     Button spawn = new Button(mainWindowShell, SWT.PUSH);
     spawn.setText("Create Child");
     spawn.setBounds(10, 10, 150, 30);
     spawn.addSelectionListener(new SelectionListener()
     {
        @Override
        public void widgetSelected(SelectionEvent e)
        {
           // =====================================================
           // on button press, create a child Shell object passing
           // the main Display. The child could also access the
           // display itself by calling Display.getDefault()
           // =====================================================
           System.out.println("Main Shell handling Button press, about to create child Shell");
           new ChildShell(display);
        }

        @Override
        public void widgetDefaultSelected(SelectionEvent e)
        {
           widgetSelected(e);
        }
     });

     // =============================================================
     // Register a listener for the Close event on the main Shell.
     // This disposes the Display which will cause the entire child
     // tree to dispose
     // =============================================================
     mainWindowShell.addListener(SWT.Close, new Listener()
     {
        @Override
        public void handleEvent(Event event)
        {
           System.out.println("Main Shell handling Close event, about to dipose the main Display");
           display.dispose();
        }
     });

     // ================================
     // Set size on main Shell and open
     // ================================
     mainWindowShell.setSize(200, 200);
     mainWindowShell.open();

     // =====================================
     // Main UI event dispatch loop
     // that handles all UI events from all
     // SWT components created as children of
     // the main Display object
     // =====================================
     while (!display.isDisposed())
     {
        // ===================================================
        // Wrap each event dispatch in an exception handler
        // so that if any event causes an exception it does
        // not break the main UI loop
        // ===================================================
        try
        {
           if (!display.readAndDispatch())
           {
              display.sleep();
           }
        }
        catch (Exception e)
        {
           e.printStackTrace();
        }
     }

     System.out.println("Main Display event handler loop has exited");
  }

  public static void main(String[] args)
  {
     new SingleDisplayMultipleShells();
  }
}