How to filter a field in the add content window in Drupal? I am very new to Drupal so I'm sorry for my lack of familiarity with Drupal terminology.

I have a content type with multiple fields (A, B, C, etc..). Each field is a selectable vocabulary list. I would like the user to select any terms in A and B fields. But I want only relevant terms to display in the C field (depending on A and B selections). In this way, A and B are independent fields and terms that appear in C are dependent.

Example:

Content type: Food dish at a restaurant

Field A: Appears on Menu type (Breakfast menu, lunch menu, dinner menu, wine list,etc.)

Field C: Appear in Menu section (Appetizers, Entrees, Deserts, etc.)

If the user selects "Breakfast Menu" for field A, it wouldn't make much sense to allow the user to select "Desert" for field C. But selecting "Appetizers" or "Entrees" would be fine. I want to filter the selectable terms in field C depending on which options are selected for field A.

Thank you for helping me out! Really :)
You can try the Conditional Fields module. It allows you to show/hide fields based on the value of other fields.

The Hierarchical Select module suggested in jimajamma's answer is meant only for hierarchically structured vocabularies. Conditional fields doesn't have a fancy animated interface like HS, but it provides more flexibility. For instance, you could make a text field depend on a taxonomy term: