Games where the player character is female and potential objects of affection are male are known as Gx B or otome games.
Sending your heart is the perfect way to break the ice with someone who's caught your attention.
The gameplay involves conversing with a selection of girls, attempting to increase their internal "love meter" through correct choices of dialogue.
The game lasts for a fixed period of game time, such as one month or three years.
When the game ends, the player either loses the game if he failed to properly win over any of the girls, or "finishes" one of the girls, often by having sex with her, marrying her (as in Magical Date), and/or achieving eternal love.
This gives the games more replay value, since the player can focus on a different girl each time, trying to get a different ending.