A field or dropdown box is a value that you can add to cards.

It could be a Task Status, Cast Rating, Date of Birth, Scene, Producer Assigned, State, or any other way that you would like to classify cards. Cards can have as many fields as you like.

A text field does not offer you an option to select, however it is a text box to write in, with the same search functionalities as a dropdown menu field value. 

You can search for fields in Project Search.

You can add and modify fields in Project Settings.