You can override JTable.editingStopped, which is invoked when editing is finished and apply your actions in that method. 
EDIT: 
JTable.editingStopped was not designed for application extension. To avoid complications, in particular platform dependent ones, a better approach is to override model's setValueAt or register a TableModelListener. Here is an example: 
import javax.swing.*;
import javax.swing.event.TableModelEvent;
import javax.swing.event.TableModelListener;
import javax.swing.table.DefaultTableModel;
public class DemoTable3 {
    private static void createAndShowUI() {
        JFrame frame = new JFrame("DemoTable");
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        Object[][] rows = { { "Column 1", "Column 2" },
                { "Column 1", "Column 2" } };
        Object[] columns = { "Column 1", "Column 2" };
        DefaultTableModel model = new DefaultTableModel(rows, columns);
        model.addTableModelListener(new TableModelListener() {
            @Override
            public void tableChanged(TableModelEvent e) {
                System.out.println("apply additional action");
            }
        });
        JTable table = new JTable(model);
        frame.add(new JScrollPane(table));
        frame.setLocationByPlatform(true);
        frame.pack();
        frame.setVisible(true);
    }
    public static void main(String args[]) {
        SwingUtilities.invokeLater(new Runnable() {
            public void run() {
                createAndShowUI();
            }
        });
    }
}
Another alternative is to add CellEditorListener to catch editingStopped events. For example: 
import javax.swing.*;
import javax.swing.event.CellEditorListener;
import javax.swing.event.ChangeEvent;
import javax.swing.table.DefaultTableModel;
public class DemoTable2 {
    private static void createAndShowUI() {
        JFrame frame = new JFrame("DemoTable");
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        Object[][] rows = { { "Column 1", "Column 2" },
                { "Column 1", "Column 2" } };
        Object[] columns = { "Column 1", "Column 2" };
        final JTable table = new JTable(new DefaultTableModel(rows, columns));
        table.getDefaultEditor(String.class).addCellEditorListener(
                new CellEditorListener() {
                    public void editingCanceled(ChangeEvent e) {
                        System.out.println("editingCanceled");
                    }
                    public void editingStopped(ChangeEvent e) {
                        System.out.println("editingStopped: apply additional action");
                    }
                });
        frame.add(new JScrollPane(table));
        frame.setLocationByPlatform(true);
        frame.pack();
        frame.setVisible(true);
    }
    public static void main(String args[]) {
        SwingUtilities.invokeLater(new Runnable() {
            public void run() {
                createAndShowUI();
            }
        });
    }
}
Also look at a Table Cell Listener by @camickr which offers custom processing of the edits.