Display Taxonomy Terms Like this

You can do this with the default core taxonomy and menu modules.

One way of doing the taxonomy is:

'gifts' as a containing vocabulary

Christmas <-- parent term (term1)
- cake <-- child terms (term2)
- flowers (term3)
- jewellery (term4)
- card (term5)
- hamper (term6)

Birthday <-- parent term (term7)
- cake <-- child terms (term8)
- flowers (term9)
- jewellery (term10)
- card (term11)

etc

When creating content, you'll see these taxonomies listed and will choose the correct tag for the gift you're creating. The cool thing about Drupal is that you could tag certain items in more than one category; for instance some jewellery could be tagged as valentines *and* mother's day.

So to view a teaser-list of *all* christmas gifts, you'd go to /taxonomy/term/1
To view a teaser-list of only christmas cakes, you'd go to /taxonomy/term/2
To view a teaser list of *all* birthday gifts, you'd go to /taxonomy/term/7
To view a teaser-list of only birthday flowers, you'd go to /taxonomy/term/9

You can create url aliases, so that /taxonomy/term/1 becomes /gifts/christmas-gifts
and /taxonomy/term/2 becomes /gifts/christmas-gifts/cakes

Now the menu. You'd basically just re-create the taxonomy structure in a menu.
The menu items will simply point to /taxonomy/term/[N] or your aliases.

One very smart thing is that, if a customer follows a link from elsewhere to /taxonomy/term/7, the menu will automatically open to that level and highlight the menu item, so the user can easily see where they are within the site's navigation.

Another smart thing is that you could make a menu link called 'all jewellery', and point it to:
/taxonomy/term/4+10+16+22 to view a teaser list of jewellery from each parent category.

Hope that all makes sense. If you're new to drupal, you may have to read the docs section on taxonomy and menus to understand what I'm talking about.