This is the standardized UI for configuring Hierarchical Select. It is used by every implementation where it makes sense to have an UI (e.g. Taxonomy has it, but Menu does not).

Preview
This is what the Hierarchical Select will look like with your current configuration.
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The description.
Saving the term lineage means saving the the term itself and all its ancestors.
This setting determines from which level in the vocabulary tree a user can select a term.
When enabled, the user will see the number of nodes that match the current term listed between brackets.
When enabled, a handle appears below the Hierarchical Select to allow the user to dynamically resize it. Double clicking will toggle between the smallest and a sane 'big size'.
Level labels
When the user is allowed to choose a term from any level in the Level choice setting, you can enter a label for each level.
However, when the user is only allowed to choose a term from the deepest level, then you can only enter a label for the root level.
LevelLabel
Root level
Sublevel 1
Dropbox settings
The dropbox allows the user to make multiple selections.
The title you enter here appears above the dropbox.
Limits the number of selections that can be added to the dropbox. 0 means no limit.
Note: the "Save term lineage" option has no effect on this, even if a lineage consists of 3 terms, this will count as only one selection in the dropbox.
This setting determines what will happen to the hierarchical select when the user has added a selection to the dropbox.
Editability settings
You can allow the user to add new terms to this vocabulary through Hierarchical Select.
Per-level settings for creating new terms.
LevelAllowTerm type
Root level
Sublevel 1
The term type you enter for each level is what will be used in each level to replace a "<create new item>" option with a "<create new term type>" option, which is often more intuitive.
Allow the user to create child terms for terms that do not yet have children.
When the user is allowed to create new levels, this option prevents the user from creating extremely deep vocabularies.