It basically means that when you write your code, you don't need to worry about there being the same name somewhere else. All your resources - nodes, params, topics and services will be in the local scope. And then you can write a top level node to include all those nodes without any problem.
Edit: (based on comment to answer)
Global:
ROS has a global namespace - "/". If you define any of your graph resource names with a leading /, they will be global names. You can have a bunch of hierarchical namespaces but as long as it starts with a "/", it is globally resolved.
Example: "/global/name/with/base"
Base:
That brings us to the second type - base names. Refer to the example above, every global name in ROS has a base which in this case is "base". You can look at it as the last name in the hierarchy and it doesn't have the "/"
Relative:
ROS also has something known as a default namespace. The default namespace can be specified but if not specified it is the global namespace - "/". Relative names DO NOT have the leading "/" and are resolved WRT this default namespace.
Example: If the default namespace were "/global/name", then "with/base" would be the relative name. Notice that there is no leading "/" to "with/base"
Private:
These names too are relative names, just that they use their nodes name as their default namespace. And they have to be specified with a leading "~".
Example: If "/global/name/with" was the name of the node, then the pvt. name "~base" would be the private name.
Please clarify how you interpret the section and why you think that's incorrect. The terms you're asking about, base, global, private, and relative, are all defined in that section.
I agree w tfoote. Anyway, detailed description below. Also maybe edit the question to include the phrase "graph resource name resolution" or something of the sort so others can find it.