Self-explanatory. In addition to having a romance, there should be humor too, often directly tied to the romance story.
Love Hina,
Aa! Megami-sama! OVA,
Chobits, and TONS more titles all fall under this genre.
Not a genre but actually a demographic. Refers to anime based on manga that was originally serialized in a magazine targeting girls of any age. American fans seem to often be confused and classify any show that has romance and/or major female main characters as shoujo-- this is wrong.
Anime based on manga targeting young women would be called josei. (though very little of the manga targetting young women gets made into anime-- the only ones I can think of are Ebichu and Momoiro Sisters.)