When you create a controlled vocabulary you are creating a set of terms to use for describing content (known as descriptors in indexing lingo). Drupal allows you to describe each piece of content (blog, story, etc.) using one or many of these terms. For simple implementations, you might create a set of categories without subcategories. For more complex implementations, you might create a hierarchical list of categories.

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The name for this vocabulary. Example: "Topic".
Description of the vocabulary; can be used by modules.
Instructions to present to the user when choosing a term.
A list of node types you want to associate with this vocabulary.
Allows a tree-like hierarchy between terms of this vocabulary.
Allows related terms in this vocabulary.
Content is categorized by typing terms instead of choosing from a list.
Allows nodes to have more than one term from this vocabulary (always true for free tagging).
If enabled, every node must have at least one term in this vocabulary.
In listings, the heavier vocabularies will sink and the lighter vocabularies will be positioned nearer the top.