As you can see on the Demo Page there are several menus where icons appear for the items. So the Vertical Menu is capable to show the icons for Joomla menu and Virtuemart type, but how to set them up is a bit different. In the following you can find detailed descriptions about how to use them.
As these menu items are coming from the Joomla core Menu Manager, the icons also can be set there. You need to edit an item, then click on the Link Type tab, and browse an icon image with the Link image parameter. Then the selected icon will appear in the menu module on the frontend.
In this case there is 2 way to get the icons for the categories of Virtuemart. If it has a category image, that one will be used, otherwise the menu will try to get an image from the category description. If none of them succeed, there won't be icon image will appear for that category.
So now you know how to set icons for the menu items, but there are several settings for them in the module manager as well.
First of all, you need to enable the icons under the Type parameters, with the Show menu-item icons parameter. Then additional settings will appear. You can set the Max-width of the icons, and also able to set its default dimensions by the Width and Height parameter. You can also set that the icon images will be just Scale down to the size you have set, or even Crop a part of the image. If you would like to have rounded corners for the icon, you can also make that by the border-radius parameter.