Look at the footnotes for the offer (follow the link at the bottom of the pages shown above. Here's part of what it says.
Companion certificate offer is only available to new Citi® / AAdvantage® cardholders approved through this offer.
Passenger is responsible for taxes, fees and charges in association with companion travel. Details as well as
certain restrictions, conditions and restricted dates apply and will be sent out on your certificate.
Tickets must be booked in V, M, L, K or W inventory. Redemption of the certificate allowed
only when used with a ticket booked by phone through American Airlines reservations or through airport or city ticket offices.
Such tickets are an additional $8 and $15 more respectively than tickets purchased through
www.aa.com The latter amounts do not apply to AAdvantage Executive Platinum® members and AAirpass® customers. All such additional amounts are subject to change. This offer expires on 2/28/06. This certificate is not redeemable for cash and has no value except when redeemed in accordance with these terms and conditions. It is also void if altered, counterfeited, obtained or used improperly or where prohibited by law.
Your companion certificate will arrive 8-10 weeks after account approval.