The description doesn't really do the story justice. The key in it is that the two main characters are entirely different people in and out of school. In school, Hori is the perfect student, popular girl, etc... Out of school she is, basically, an over worked "housewife" (sans the husband or actually being the parent of the child she cares for), taking care of her younger brother, cooking, cleaning, and a mad woman in terms of getting the best supermarket deals. Meanwhile Miyamura is the introverted, glasses wearing student at school, but outside of school he is a tattooed, multiply pierced hottie with a heart of gold. He also, counter-intuitively, doesn't get good grades, which is used for much humor. (Introverted guys with glasses are supposed to be top students, no?)
Also, this description is not entirely accurate either:
"Honoka Sawada, the girl next door who is attracted to Miyamura."
Based on the Horimiya manga (story by HERO and art by Daisuke Hagiwara) the character of Honoka seems to have a crush on Miyamura at first, but in reality has yuri crush on Hori. At the point in the manga I have been able to read, it appears that she may start thinking of Miyamura as an older-brother type figure, and I suppose she could end up crushing on both of them...
I really wish they would do an anime of Horimiya, which has much better art and, from what I've read, a more romance oriented emphasis. It is a really great manga!