Why would you not use a <form> ? all other methods consist of using jquery in combination with ajax, or just ajax for sending the values. But there shouldn't be a reason to not use a <form> tag.

First, you need to include form tags:

<form action="process.php" method="post">
    //form content
</form>

Change your submit button. It's also good to change the name to somthing other than "submit" to avoid namespace conflicts:

<input type="submit" name="sub" class="btn btn-large btn-block btn-primary" value ="Submit" />

Also, give your selects different names (You have two with the name "topic"):

<select id="meat" name="meat">
   <option value="hotdog" name="nhotdog">   hotdog     </option>
   <option value="sausage" name="nsausage"> sausage    </option>
</select>

And then retrieve those values from $_POST:

$meat = $_POST['meat'];

In #box3 you have 2 selects with the same name.

Try something like:

<select id="meat" name="meatSelect">
<select id="fruit" name="fruitSelect">

And then:

$meatSelect = $_POST['meatSelect'];
$fruitSelect = $_POST['fruitSelect'];

I always thought that you have to use the -tag if you want to submit data just with submit button. An alternative is to take a button and use javascript / jquery to read data from fields and submit them via get-parameters with an url. However it seems you would like to go the classic / easy way. So you need the and define the method and action.

In addition a little hint: Try to use a php framework with mvc-(model view controller)pattern. When you use it in the right way it makes you easier to handle your code, brings predefined functions / classes and makes your functions against database safer. An example for such a framework would be codeigniter but there are many more...

Please see below code:

 <script src="http://code.jquery.com/jquery-1.9.1.js"></script>
 <script type="text/javascript">
 $(document).ready(function()
 {
 $(button).click(function() {
var name=$("#name").val();
 var frt=$("#fruit").val();
var gender = $("#gender").val();
var topic= $("#topic").val();
var descr= $("#description").val();
 var dataString = 'name='+name+'fruit='+ frt+'gender='+gender+'topic='+topic+'desc='+descr;

$.ajax
({
type: "POST",
 url: "ajax.php",
data: dataString,
  cache: false,
success: function(html)
{
$("#success").html(html);
} 
});

 });
});
</script>

You should add id in all dropdown fields. also add which you want to view the show success or error result

<div id="success"></div>