I'm the one who cracks the whip and holds the upper hand.
I'll beat you, mistreat you, till you quiver and quail.
The female of the species is More Deadly Than the Male."
This character is a female whose defining trait is that she is Dominant in the BDSM sense of the word. She is very likely to be sexually dominant (ethically or unethically), but doesn't have to be. Instead of being overtly sexual, she might be a dominatrix in a nonsexual way of Playing to the Fetishes. For example, she might be an animal tamer who use her skill on humans for plot purposes.
The typical Dominatrix will wear a very strict (yet usually quite revealing) uniform and carry a whip or similar tool. Her clothes are usually made from leather or rubber, and often include thigh high boots. Don't be surprised if she takes a dominant attitude to almost everyone at almost all times...actually, be grateful if it stays at "almost". However, expect some people to make sure to misbehave around her.
Simply being sexually dominant does not make a female character into a dominatrix. It must be her defining trait, and overtly so.
Also, the character doesn't have to be an actual character: One variation of Good Angel, Bad Angel is to replace the angel with a woman dressed to look sweet and romantic and the devil with a woman dressed like a dominatrix.
In a way, every Dominatrix is a fictional character...and this includes dominatrices in Real Life. Even when a sexually dominant woman has the dominance as her primary sexual identity, it's still just one of her many traits - not the one thing that defines her. The dominatrix, on the other hand, is a professional whose role is to fulfill a masochistic fantasy. This might be considered a kind of sex work, but most dominatrices do not include sex or any form of nudity or physical contact in the services they provide. In fiction, however, a Dominatrix character does not have to have a job at all. Or anything else that might distract her from the plot (or lack thereof). If she does have a job that is not related to sex or taming, she's probably living in a Fetish-Fuel Future compatible with being dominatrix at work anyway.
See also Dressed Like a Dominatrix, for characters who wear costumes inspired by them despite ostensibly not being an actual dominatrix.
No Examples, Please