Companion Ticket, also called companion fare, companion certificate, companion pass, etc. is a Promotional Airfare under which a second ticket (for the same flight and for the same date) is sold at a discount and sometimes even Free. Usually these tickets/certificates come with lot of restrictions like minimum ticket price of the paid ticket, advance purchase requirements, other fees and even blackout dates. The terms and condition varies by the issuer.
IMHO, Companion Ticket offered by Alaska Airlines is probably the best out there – Sold for $99, it’s good on any fare, from cheapest in the market to first class, there are no blackout dates or other restrictions, and the companion ticket counts as the same booking class as the paid ticket. It earns miles, is eligible for upgrades, etc. Suggestion – use it to fly first class for longer flights to get the maximum value out it.