Since you didn't post a sample of what you're working with I created an example that tries to cover a few different scenarios.
<ul id="list">
<li><input type='checkbox' id="check1" name="check1" value="hello" /> Checkbox #1</li>
<li><input type='checkbox' id="check2" name="check2" /> Checkbox #2 <a href="#">hello</a></li>
<li><input type='checkbox' id="check3" name="check3" /> Checkbox #3</li>
<li><input type='checkbox' id="check4" name="check4"/> Checkbox #4</li>
</ul>
<button id="output"></button>
On button click...
$("#output").bind("click", function(){
// can be any jQuery selector -- for this example we use #list
$("#list").find("input[type='checkbox']:checked").each(function(){
var $t = $(this), // current checkbox
$p = $t.parent(), // parent li - define more so w/ parent('li')
text = $p.text(), // text of li
val = $t.val(), // checkbox value
id = $t.attr('id'), // checkbox id
name = $t.attr('name'), // checkbox name
children = $p.children("a:first").text(); // select first child anchor element->get text
// insert magical code here...
// print to console for debug
console.log($t, $p, text, val, id, name, children);
});
});