$.ajax( type: "POST" POST method to php

try this

$(document).on("submit", "#form-data", function(e){
    e.preventDefault()
    $.ajax({
        url: "edit.php",
        method: "POST",
        data: new FormData(this),
        contentType: false,
        processData: false,
        success: function(data){
            $('.center').html(data); 
        }
    })
})

in the form the button needs to be type="submit"

You need to use data: {title: title} to POST it correctly.

In the PHP code you need to echo the value instead of returning it.

Check whether title has any value or not. If not, then retrive the value using Id.

<form>
Title : <input type="text" id="title" size="40" name="title" value = ''/>
<input type="button" onclick="headingSearch(this.form)" value="Submit"/><br /><br />
</form>
<script type="text/javascript">
function headingSearch(f)
{
    var title=jQuery('#title').val();
    $.ajax({
      type: "POST",
      url: "edit.php",
      data: {title:title} ,
      success: function(data) {
    $('.center').html(data); 
}
});
}
</script>

Try this code.

In php code, use echo instead of return. Only then, javascript data will have its value.