I have done this in the past by creating a template within my theme called subcategorylist.phtml in template/catalog/product/
<ul class="list">
<?php
$currentCat = Mage::registry('current_category');
$subCats = $currentCat->getChildren();
foreach(explode(',',$subCats) as $subCatid)
{
$_category = Mage::getModel('catalog/category')->load($subCatid);
if($_category->getIsActive())
{
$catUrl = $_category->getURL();
$catName = $_category->getName();
if($_category->getImageUrl())
{
$catimg = $_category->getImageUrl();
}
echo '<li><a href="'.$catUrl.'" title="View the products for this category"><img src="'.$catimg.'" alt="'.$catName.'" /></a>';
echo '<h2><a href="'.$catUrl.'" title="View the products for this category">'.$catName.'</a></h2></li>';
}
}
?>
</ul>
then within magento backend in CMS -> Static blocks add a new block called Categories with the following code
{{block type="catalog/product" template="catalog/product/subcategorylist.phtml"}}
Then you can go to the particular category you wish to implement this on go to display settings and select the Categories block from the CMS Block drop down.