I'm going to try to update this based on the code you provided. Your script tag contents should be this:
<script type='text/javascript'>
$("#product_description_product_1, #product_description_product_2, #product_description_product_3").change(function(){
concatenated_string = $("#product_description_product_1").val() + $("#product_description_product_2").val() + $("#product_description_product_3").val();
$("#product_description_product").val(concatenated_string);
})
</script>
Also your hidden field tag should look something like this (I'm assuming the top line, of the second block of code, was intended to be the hidden field):
<input type='hidden' value='' id="product_description_product">
Here is a jsfiddle with this an example as well http://jsfiddle.net/eNNZX/
Please keep in mind the div with id "temp_display" is not required, its only so you can see the value after each change.
This way anytime any of the selects are changed the hidden input is updated with the concatenated version of all 3. Then when you submit the page, just look at the parameter referencing the hidden input for your desired value.
Hope this helps!