invoking a block and attaching it to a specific html element
You can achieve this by creating a custom module which prints block content as shown below:

&lt;?php
function mymodule_menu(){
    $items = array();

    $items['ajax/replace/block'] = array(
        'title' =&gt; t('Ajax Block'),
        'page callback' =&gt; 'ajax_callback',
        'access callback' =&gt; true,
        'type' =&gt; MENU_NORMAL_ITEM
    );

    return $items;
}

function ajax_callback(){
    $block2 = module_invoke("block", "block_view", 1);
    print $block2["content"];
}


Then add following jQuery line in your page to replace the target element with block content:

jQuery("#target-selector").load("/ajax/replace/block");