jabrister wrote: In the CB configuration manager (near the bottom), what does "list of types to allow your users to further categorize their connections" mean/do/how do I use it?

I assume you mean in the Connections tab of the CB Configuration.

This is a list of connection types that your users can choose to characterize a connection they make.

You can add new types by typing them in the text box (one per row).

Splitting up questions below ...

jabrister wrote: Yes. How does a user "characterize" a connection they make?

When user accepts a connection or later when they go to their Connections -> Manage Your Connections menu item in their user profile they will see a row for each connection - the second column is the Type selection that shows them the available connection types they can choose for each connection. The user can select more than one type using the control/cmd key.

What does that mean?

A user can characterize his connections tagging them against one or more of the predefined (by admin in backend CB configuration area) connection types.

Where is that a choice for the user to choose from?

Connections menu (see first answer).

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How is it accessed in the site?
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Currently the most important aspect of this (besides the displaying) is that the Privacy plugin (installed and configured separately) allows you to specify which connection type can view a privacy protected field of tab.

How is it displayed in the site?

Users visiting their connections tab can hover over a connected avatar and see the selected connection type (if one has been selected).

How can I associate that with respect to classifying my users into groups that I want them to be in when they register? If I want users in one group (group 2) to have further classifications that users in another group (group 1) can search for within, how can I accomplish that?

Nope, connection types are just used to classify connected users. It is not a grouping function as you describe.