In summation, a "black belt" "says" whatever the people in charge of your martial art says that a black belt says.
This is the bottom line, in practical terms. Unfortunately, those "in charge" may have no respect for what a black belt is supposed to mean, or have a false sense of what proficiency in TMA (in my case, karate) should mean. This is most likely due to how they were taught. Their teacher probably had low expectations, and so a downward spiral of quality is passed on. Or, the guy in charge might just put greed ahead of quality.
In ideal terms, a black belt should mean that, whatever the style, the student should have 90% of the techniques down pat so they can be used effectively in a real life situation. This means good control, form, speed, power, balance, flow, timing, tactics and other elements that make the art actually work at a high level.
The best way to judge this is to measure yourself against your peers, by observing other schools, or by competition, or ask other teachers to evaluate you. Walk into another school with a white belt, and the fact that you are a black belt should be quickly recognized by your peers. If not, you may need to re-evaluate the meaning of your black belt and apply yourself to improve.
Then there are the non-physical elements that IMO should be an integral part of getting a black belt: Perseverance in overcoming weaknesses, injuries or failures, dedication, some philosophical and historical understanding of the origins of the art, a moral imperative to use the art to aid others, and so on. These are just a few random thoughts on the subject, hopefully nothing new for most of you.
A first degree black belt is, indeed, the beginning of the road to mastering one's self and finding the art is richer than one's ego. Few new black belts are at this stage. Patience and humility are also things that usually come after that first exhilarating promotion to black as you progress in degrees. But that's where the real payoff is.