The Nameless Card has unknown abilities, but is cited as the representation of Sakura's love for Syaoran Li (CCS). In the English dub, The Nameless Card was called 'The Hope' and caused confusion when naming the actual Hope card for the dub. It is under no other card as it was an original Sakura Card created by Sakura herself with (presumably) Star Magic. Thus, there was no disturbance in the balance of the negative and positive energies created between the original Clow Cards and the ones that were transformed into Sakura Cards/Star Cards.
Its spirit form is never shown, but it is most likely that it is exactly like/similar to the picture depicted on its card, that of a winged heart with a crown on top.
It is unknown what the exact powers of The Nameless Card are, since it was created near the end of the final episode of the anime. This card does gain more screen time during Cardcaptor Sakura Movie 2: The Sealed Card, in which it resolves the conflict of the movie by fusing with The Nothing to form The Hope.
From this act alone, many theories can be made about this card's power. One such theory is that it gives hope.
The Nameless Card first appeared in Episode 70. It started when Sakura felt sad about Syaoran returning to Hong Kong since there was no longer a need for him to be in Tomoeda. Then when she realized her true feelings for Syaoran, The Nameless Card appeared through the floor and landed in her hand. The card was fully shown at the end of the episode, after Sakura promised Syaoran she'd see him again.
The Nameless card merged with The Nothing in the second movie. Eriol had told Sakura that to seal The Nothing, someone would have to sacrifice their most important feeling. When Sakura demands that The Nothing change, it chose Syaoran to lose his most important feeling. Syaoran's most important feeling is his love for Sakura but told her not to worry because he would just "fall in love with (her) again". When The Nothing attempted to take Syaoran's feeling, The Nameless Card intevened, saving Syaoran. As a result of The Nameless Card's intervention, it merged with Nothing to create The Hope. Since The Nameless Card is a creation and representation of Sakura and Syaoran's love for each other, we do not know if it would have intervened The Nothing chose to take the most important feeling of anyone other than Sakura or Syaoran.