Refresh table data with Ajax

In wordpress you need to use ajax in a specific way to follow the standard
https://codex.wordpress.org/Plugin_API/Action_Reference/wp_ajax_(action)

create a function in your functions.php file to handle the data retrieval and/or display of the table and add a hook to wp_ajax_(fires only for logged in users) and wp_ajax_nopriv_(fires for guests as well)

add_action( 'wp_ajax_add_foobar', 'prefix_ajax_add_foobar' );
add_action( 'wp_ajax_nopriv_add_foobar', 'prefix_ajax_add_foobar' );

function prefix_ajax_add_foobar() {
    // Handle request then generate response using WP_Ajax_Response
    //generate table data and build table html here

    // Don't forget to stop execution afterward.
    wp_die();
}

once added to the functions.php page you can then include the JS in your script page or in a seperate file

jQuery.post(
    ajaxurl, 
    {
        'action': 'add_foobar',
        'data':   'foobarid'
    }, 
    function(response){
        alert('The server responded: ' + response);
    }
);

So the ajaxurl action refers to your action registered in wordpress after wp_ajax_ or wp_ajax_nopriv_. If you register it like this wp_ajax_nopriv_fill_my_table your ajaxurl action will be fill_my_table

I would also suggest here to make the ajax call in a JS function so that you can call the same function at (document).ready()
Here is another post where it is well answered and relates to your question
:
Jquery ajax to custom php file: returning blank data