What are field options?
I may not quite understand the question. When you create a Field, if you set it to eg Select or Radio, then you get to create, or choose an existing set of field options, eg apple, banana, carrot.

Once created, you can access these to modify them either via the field itself, or via Admin > System Settings > Option Groups, or at civicrm/admin/options?reset=1

Documentation: best page i can see in book is this one, search for 'multiple choice options' on that page. Maybe documentation needs to be improved so Search for 'Option Groups' offers this page - something you could offer to do as an active member of this open source community?

GENERAL NOTE: these options belong to the Custom Group, which can then be 'used' in a Profile. You do not create or modify them in the Profile directly. Newcomers to civicrm often find it confusing as 'fields' are used in Profiles, and some aspects of them, eg title, pre-help, can be changed in the profile. But the Fields itself is created/modified via Custom Fields.