Social Links are a means of representing your character's bonds with other characters, and are the way in which characters unlock new Personas for use. To gain Social Links, a character must engage in RP with other characters.
Each character can expend up to four Social Link points to other characters per week. An exchange of links is mutual; you gain a point in the arcana of the character you exchange a link with, and they yours. At every ten points in an arcana, you will unlock a new Persona in a given arcana.
Free Tarot, which can be gained from various means including public or admin-run scenes, are effectively points that can be placed in any arcana you choose.