Reseda first appeared to the Hellsing organization as a cat. She was looking for news of Helena, but in the meantime was adopted by Seras as a pet.
She's actually a chordewa - a Bengali type of vampire which favors cat form, but can be distinguished from a normal cat by its odd way of mewing. Though careful not to meow around the older and more experienced Hellsing members, Reseda was found out when Seras mentioned her strange sound to Walter.
Another notable ability of chordewas: if one licks your lips, you subsequently die. Aside from that, Reseda is very much like your average True Undead. Like Alucard, she enjoys a good fight; fortunately for both of them, she's strong enough to hold her own against him for a while, so they have some fun beating the tar out of each other.
Reseda's more relaxed and casual than Alucard, and tends to disregard anything that doesn't interest her. This includes most humans (much to Integra's annoyance, although she'll cheerfully accede to Integra's directions if she feels like it). Her un-life so far has been largely spent wandering around looking for interesting things.
A bit of her history: She was born on the Isle of Man (origin of the Manx cat) in the late fourteenth century. Since becoming a chordewa she's lived a fairly solitary and hedonistic life. She likes to travel, and has encountered both Alucard and Helena before.
While Helena's filled her un-life with books, and Alucard with battles, Reseda is less focused; she'll get absorbed in anything that catches her fancy. Most of it doesn't last, and as a result she's adopted an uncaring attitude, able to let go without much thought. Helena, being apparently as everlasting as herself, was an exception. I'll write their backstory one of these days.
A bit of her real-world history: I created Reseda in 1998; she was my first Mary Sue (oh, the nostalgia), written for a Sailor Moon fanfic. When I first saw Hellsing in 2002, I thought it was incredibly cool but very creepy. The Reseda voice in my head, on the other hand, enjoyed it immensely; so I decided to write her into a Hellsing fanfic one day.
I've been fighting to un-Sue Reseda ever since her creation, with limited success; her Shine incarnation cuts it close on the test, and has gotten mixed results on the reader poll (at left). She hasn't returned to Shine since her introduction, but she'll be back for more character development later. As Scott Adams said, that's the only way to overcome complaints about characters.