That's a custom piece of code they appear to be using on that page unless they're just using the bbcode ([ i m g ] tag) in the category description field, which should basically do the same you're up to without needing to fiddle with the code.
I can't remember having seen custom code posted anywhere that does exactly what you're up to, so here goes: Edit themes/yourtheme/theme.php, find// HTML template for the category list
$template_cat_list = <<<EOTand edit the stuff benaeth it as you see fit. If that piece of code doesn't exist in your custom theme, copy// HTML template for the category list
$template_cat_list = <<<EOT
<!-- BEGIN header -->
<tr>
<td class="tableh1" width="80%" align="left"><b>{CATEGORY}</b></td>
<td class="tableh1" width="10%" align="center"><b>{ALBUMS}</b></td>
<td class="tableh1" width="10%" align="center"><b>{PICTURES}</b></td>
</tr>
<!-- END header -->
<!-- BEGIN catrow_noalb -->
<tr>
<td class="catrow_noalb" colspan="3"><table border="0"><tr><td align="left">{CAT_THUMB}</td><td align="left"><span class="catlink"><b>{CAT_TITLE}</b></span>{CAT_DESC}</td></tr></table></td>
</tr>
<!-- END catrow_noalb -->
<!-- BEGIN catrow -->
<tr>
<td class="catrow" align="left"><table border="0"><tr><td>{CAT_THUMB}</td><td><span class="catlink"><b>{CAT_TITLE}</b></span>{CAT_DESC}</td></tr></table></td>
<td class="catrow" align="center">{ALB_COUNT}</td>
<td class="catrow" align="center">{PIC_COUNT}</td>
</tr>
<tr>
<td class="tableb" colspan="3">{CAT_ALBUMS}</td>
</tr>
<!-- END catrow -->
<!-- BEGIN footer -->
<tr>
<td colspan="3" class="tableh1" align="center"><span class="statlink">{STATISTICS}</span></td>
</tr>
<!-- END footer -->
<!-- BEGIN spacer -->
<img src="images/spacer.gif" width="1" height="7" border="" alt="" /><br />
<!-- END spacer -->
EOT;from themes/sample/theme.php into a new line before?>of themes/yourtheme/theme.php and then edit this stuff. You will have to come up with some custom PHP code that determines what picture to display. Something like// HTML template for the category list
$template_cat_list = <<<EOT
<!-- BEGIN header -->
<tr>
<td class="tableh1" width="80%" align="left"><b>{CATEGORY}</b></td>
<td class="tableh1" width="10%" align="center"><b>{ALBUMS}</b></td>
<td class="tableh1" width="10%" align="center"><b>{PICTURES}</b></td>
</tr>
<!-- END header -->
<!-- BEGIN catrow_noalb -->
<tr>
<td class="catrow_noalb" colspan="3"><table border="0"><tr><td align="left">{CAT_THUMB}</td><td align="left"><span class="catlink"><b>{CAT_TITLE}</b></span>{CAT_DESC}
EOT;
//your custom code here that determines what image to display for which category. For demonstration purposes, I have added a simple if/then construct
if ($cat==1) {
$template_cat_list .= '<img src="your/first/category/image.jpg" border="0" width="50" height="100" alt="" />';
} else {
$template_cat_list .= '<img src="your/second/category/image.jpg" border="0" width="50" height="100" alt="" />';
}
$template_cat_list .= <<<EOT
</td></tr></table></td>
</tr>
<!-- END catrow_noalb -->
<!-- BEGIN catrow -->
<tr>
<td class="catrow" align="left"><table border="0"><tr><td>{CAT_THUMB}</td><td><span class="catlink"><b>{CAT_TITLE}</b></span>{CAT_DESC}</td></tr></table></td>
<td class="catrow" align="center">{ALB_COUNT}</td>
<td class="catrow" align="center">{PIC_COUNT}</td>
</tr>
<tr>
<td class="tableb" colspan="3">{CAT_ALBUMS}</td>
</tr>
<!-- END catrow -->
<!-- BEGIN footer -->
<tr>
<td colspan="3" class="tableh1" align="center"><span class="statlink">{STATISTICS}</span></td>
</tr>
<!-- END footer -->
<!-- BEGIN spacer -->
<img src="images/spacer.gif" width="1" height="7" border="" alt="" /><br />
<!-- END spacer -->
EOT;should do the trick.
However, as you appear to be a newbie, I suggest using the bbcode solution.
Joachim