The umbraco back office is the area you are logged into at http://example.com/umbraco/ . This is the place where you administer your site, create content nodes, manage users, etc. You can also manage your templates and style sheets.
Back office extensions are packages in which other users have expanded the functionality of the back office. This includes custom data types (things that you add to document types to collect data from users when creating nodes), such as Google Maps DataType, or tools and utilities that make life easier in the back office, such as FALM Cleaning .
Regarding your comment:
There may be several solutions to the problem.
Will a product ever have more than one category? If not, you can create a category document type and simply create new product nodes under each node category. Your macro will simply list all service nodes.
Otherwise, you can put the data type in the product document type, which allows you to select categories for it. Most likely, there will be a fairly multi-segment list or list of flags. If the client wants to control which categories are available in this case, you can use XPath CheckBoxList . The macro for this scenario simply listed the available categories, and when you click on the node category, you will have another macro that filters products based on their categories.