Card#0 also known as The Fool. This card represents the social link of the investigation team. The social link is upgraded through out the game as you make progress.
Card#1 also known as The Magician. This card represents the social link of your friendship with Yosuke Hanamura. The social link is upgraded when you spend time with Yosuke.
Card#2 also know as The High Priestess. This card represents the social link of your friendship with Yukiko Amagi. The social link is upgraded through spending time with Yukiko.
Card#3 also know as The Empress. This card represents the social link of your friendship with Margaret. This social link is upgraded when you visit Margaret in the velvet room and show her the persona she asks for with the ability she asks for.
Card#4 also known as The Emperor. This card represents the social link of your friendship with Kanji Tatsumi. The social link is upgraded through spending time with Kanji.