I really like it for grouping related objects together despite hierarchy changes.
Let's take an example here:
var/count = 0, obj/item/i
var/list/conts = user.contents.Copy(), take = list()
i = locate(ingredients[count]) in conts
take += i
conts -= i
user.contents -= take
var/count = 0, /obj/item/i, t
t = results[count]
i = new t(user)
Normally, we'd define all /obj/item subtypes under the /obj/item path and all the recipes under the /recipe path. This means if we want to modify an item and its recipe, we need to jump around in DM to find both the recipe definition and the item definition.
The "/" operator allows you to specify path nodes. But if a path begins with the "/" operator, that means that the node is a root. What does this mean?
Well, it means that we can arbitrarily swap to other paths when we're tabbed inside of another path.
ingredients = list(/obj/item/mushroom,/obj/item/water)
results = list(/obj/item/potion)
Even though /recipe/potion is tabbed inside of /obj/item/potion, because we prefaced "recipe" with "/", the tabbed-in prototype is ignored and we go back to root. That means even though /recipe/potion is tabbed inside of /obj/item/potion, we're actually defining the properties of /recipe/potion without affecting /obj/item/potion hierarchy.
This is really useful for defining interface elements that work as part of a datum, and subelements of multi-part systems.
While this is documented, I found the example in the reference really quite terrible.