Each time the button is clicked you are creating a new DefaultListModel and adding the element to this brand new list. Therefore you cannot add them all into the same list.
Instead define your DefaultListModel model1 outside of addActionPerformed
method and use the reference to the object inside like the following:
DefaultListModel model1= new DefaultListModel();
private void addActionPerformed(java.awt.event.ActionEvent evt) {
model1.addElement(desc.getText());
jList2.setModel(model1);
jList2.setSelectedIndex(0);
desc.setText("");
}