Hide portions of form until prior part is filled out?

Yes, you're referring to the conditional logic feature. If you click on a field and open the options panel, click over to the "advanced" tab and you'll see a checkbox to "enable conditional logic". If you check that, you'll see more fields that will let you show or hide the field based on the value of another select box, multiple choice or checkbox field.

screenshot

If you group sections of content together under a section header element, you can show/hide whole sections at a time.

The new documentation isn't quite ready for release so there's not a lot of real thorough information available yet..

http://www.gravityhelp.com/documentation/form-fields/section-break/

You can enable conditional logic for the section break and the content underneath it will inherit from it's visibility.

screenshot

Basically, the conditional logic will show/hide the all the content under the section break until it either gets to a new section break, or the end of the form.

http://www.gravityforms.com/demo/gravity-forms-conditional-logic-form-demo/

Select an option from the field at the bottom "Who Would You Like to Contact?" and you'll see whole sections of content show/hide based on the value.

The conditional logic only works on the pre-defined values in either select boxes, checkboxes or multiple choice (radio) fields. It doesn't work based on the value of a text field.