HTML:

<dl id="feature-list">
    <dt id="basic" class="category-name">
    <dd id="basic-toggle" class="category-recepient">
        <div class="feature">
            <div class="feature-content">
            <input id="checkbox1" type="checkbox">
        </div>
        </div>
    </dd>
    <dt id="options" class="category-name">
    <dd id="options-toggle" class="category-recepient">
        <div class="feature">
            <div class="feature-content">
            <input id="checkbox2" type="checkbox">
        </div>
        </div>
    </dd>
</dl> 

JQUERY

$('input').change(function () {
    var value = $(this).closest("dt");
    //do something with value.id
});

$(this).closest("dt") returns the checkbox instead of <dt id="(category)" class="category-name">

I tried $(this).closest(.category-name), $(this).closest("dt").find(.category-name)