The Soul Brotha is a stereotypical "urban" black person. Unlike certain other racial stereotypes, this one usually isn't hateful or mocking. To the contrary, these characters are often portrayed as "cool" and "badass", and are admired both in-universe and by fans (if done well; if not, it may result in an Ethnic Scrappy). Still, a stereotype is a stereotype, and at its core it still stems from the conscious or subconscious belief that black people are somehow "different" and that their "blackness" should be one of their main characteristics.
The exact way this character type is portrayed may vary. In The '70s, especially in Blaxploitation films, they often wore garish "funky" clothes and afros (usually of the asskicking variety), while in The 2000s and The New '10s they go for a stereotypical "gangsta" getup, complete with golden chains, tattoos, do-rags and dreadlocks. There's also the occasional pimp in a purple pimp suit, fur coat, feathered hat and cane, or a rich rapper who usually is a Shallow Parody of whichever hip hop artist is popular at the time. They can be an Angry Black Man, a Scary Black Man, a streetwise comedic sidekick, or even a Malcolm Xerox. They speak in Jive Turkey, and often have a Ghetto Name. If the media in question touches sexual themes, expect Where Da White Women At? and Black Is Bigger in Bed to come into play.
Women aren't exempt from this trope either. A Soul Sista also dresses in a stereotypical way and speaks in Jive Turkey. She's usually a Sassy Black Woman, and is even more likely to end up with an exaggerated Ghetto Name.
A lot of times, a black character will be mostly portrayed non-stereotypically, but still exhibit a couple Soul Brotha / Sista traits.
Expect a Black Best Friend, a Captain Ethnic, or a token black character in general to be this trope. Some stock black character types, however, e.g. Bald, Black Leader Guy and Black Boss Lady, generally tend to avoid this trope altogether.