Heir: Someone who inherits their aspect by being given it, and/or representing/becoming their aspect, physically or metaphorically. They start out with their aspect affecting and controlling them on its own will, being saved or helped by their aspect when they’re in trouble, and eventually learn to consciously control it as they “inherit” it.
Heart: Basically soul, the essence of someone's being, and someone's emotions and motivations. It's speculated that it's also related to intuition. Heavily associated and likely directly tied to romance and relationships.
An Heir of Heart starting out would be someone who just kind've ends up stumbling into friendships and relationships that will be really important to the story. They'd meet people by coincidence and have a sense that leads them to suspecting that they should get to know that person better, even if it seems at first like they wouldn't really get along. As the game goes on, they'd forge a strong emotional bond with everyone in their game. They wouldn't be a leader by any means but would be a huge morale booster. Or the opposite. Depends on their relationship with a given person.
As they actually go through the process of inheriting their aspect, they'd directly and intentionally manipulate people's emotions. They'd deeply understand people's souls and know how to influence them on a deeper level than just emotionally. They'd have the power to really impact a person's psychology, changing them as a person. For better or for worse.
They'd also likely be uh. Very desirable. It'd be fitting for a Heir of Heart to have a lot of people crushing on them after they reach their full development.