If a "harem" anime features one man surrounded by female love interests, a "reverse harem" features one woman surrounded by male love interests. Prototypical reverse harems: Ouran High School Host Club, La Corda d'Oro, Fushigi Yugi.
The Harem theme in manga and anime has classically involved a single male protagonist that is surrounded by a number of female characters that was buying for his affections. A Reverse Harem is just as the name implies. All the roles are reversed. These stories involve a female protagonist surrounded by a number of males. It's a popular theme in Shoujo and romance novels targeting a female audience.
The main female lead might find guys who do bad things for attention, attractive. They often think that they can tame the beast.
Examples: Blood Dupre,
Hot guys or popular guys who are too good for the main female lead.
Examples: Tamaki Suou,
He can be a close friend, a butler, a slave, or a care taker of the female lead during her childhood.
In rare occasions, the main female lead will develop a romantic relationship with another woman.
Example: Queen Vivaldi,
These guys are bold and assertive and can serve as unwanted attention.
Examples: Peter White,
He does not want company or does not know how to interact with other people. Sometimes, they're outcasts shunned by society.
People who wear glasses.
Examples: Julius Monrey, Pace,
The female lead might prefer an older and mature gentlemen.
Sometimes, two is better than one.