EDIT: This answer was submitted before the OP's jsFiddle example was posted in question. See second answer for response to that jsFiddle.
Here is an example of how it could work:
HTML:
<div id="someDiv">
Once upon a midnight dreary
<br>While I pondered weak and weary
<br>Over many a quaint and curious
<br>Volume of forgotten lore.
</div>
Type new text here:<br>
<input type="text" id="replacementtext" />
<input type="button" id="mybutt" value="Swap" />
<input type="hidden" id="vault" />
javascript/jQuery:
//Declare persistent vars outside function
var savText, newText, myState = 0;
$('#mybutt').click(function(){
if (myState==0){
savText = $('#someDiv').html(); //save poem data from DIV
newText = $('#replacementtext').val(); //save data from input field
$('#replacementtext').val(''); //clear input field
$('#someDiv').html( newText ); //replace poem with insert field data
myState = 1; //remember swap has been done once
} else {
$('#someDiv').html(savText);
$('#replacementtext').val(newText); //replace contents
myState = 0;
}
});