Princess Koiko has the power to use a Love Love Beam. And the story revolves around this special power, but its functionality is very badly explained. Her kingdom lives in peace because of this power (somehow). This power is passed down within the royal family, but she'll lose the power once she gets married (somehow). Her power seems to make most people love her and become compliant to her wishes, but makes Ginjirou reminisce about his lost love Ohana and doesn't seem to affect Shirou at all (with no clear explanation as to why these cases are different, or for that matter what the Beam is actually doing). There is a creature named Chu which is the spirit of a staff which is related to the beam (but the nature of the spirit and the staff and their exact relation to the power isn't entirely clear).
The actual plot largely revolves around her having an arranged marriage, but running off after Shirou because she loves him and wants to be with him. She runs into Ginjirou, a thief who also has a star-crossed lovers type situation and wants to help him, but seems to just make things worse. Shirou is following her journey while disguising himself as various people she meets along the way. He also uses some sort of memory-alteration technique to make her think that people around her have been dying, when actually they weren't. In other words, he wanted her to be traumatized and guilt-ridden...and he supposedly loves her. I can't say that I understand his motives.
I think the biggest problem with this manga is that it doesn't have good exposition. It could be an issue with the translation, but I think it's more likely it's an issue of the author just glossing over important things and trying to include too many twists and turns, but not making them clear along the way.