Does "nonrefundable" mean that if a flight is paid for and not taken that the price of the missed...

Yes. You cannot get your money back. But, you can pay a penalty to changeit ($150.-250. plus) and you make up any difference in airfare. Not worth it if you think you will have to change your plans. In any event, buy travel insurance because you never know what could come up in the meantime. You will pay extra for it but will be able to get your money back.

If You have a medical reason for not being able to take the flight and have a doctors note, the charge is only $50 deducted from your ticket cost...

Nick,
Here are the rules for a non-refundable ticket:

You can cancel a wholly unused ticket any time prior to departure by calling 1800 united1. Or you can cancel at United.com, center of page VIEW RESERVATION, enter passenger last name and confirmation number. That takes you to a page with several options including CANCEL.
If you purchased a refundable (read expensive) ticket you can get a refund of your money. Most bargain tickets are non-refundable, however you can make changes for a penalty and any difference in fare. If you call 1800 300 1547, these agents can help you find a date that is about the same price as your original ticket. In the domestic USA market the change fee is usually $150 per person paid when you are ready to make new reservations.
Once you cancel your current itinerary, you have one year from date of purchase to make a change and pay the change fee, and you can plan out 330 days in the future. Do not lose your confirmation number, as you will need it when you decide to reschedule your travel. Your cancelled ticket will remain in the system for one year from date of purchase. Ask the agent when that year is up and they will let you know.
If cancellation is due to illness or emergency of you or your immediate family. You can qualify for a reduced change penalty ($50pp) with proper documentation (Dr note, hospital bill, or program from a funeral).