The first photographic image was black and white. Everyone -- pros and snapshooters -- shot primarily black and white for photography's first 100 years, even after the invention of "mass" color imaging (Kodachrome) in the 1930s. Black and white died almost over night in snapshooting when color film and processing cost the same as black and white (eventually, color was actually cheaper). But, among serious imagers, black and white stayed popular. This was partly driven by the ability to further refine exposure, control contrast and selectively "burn" and "dodge" prints in the darkroom (you could do it in a color darkroom, albeit not as easily).
Today in the digital age, black and white has zero advantage over color with respect to cost or to post processing. Yet, black and white remains. It's common in portraiture, and very common in fine art imaging. Editorial fashion uses it, too.
I suppose every artist has a different opinion as to why black and white survives, and perhaps they're all correct. I think it's because when you look at a black and white image, color doesn't distract from the shapes, textures and gray shades. This heightens drama, and we infer feelings that differ from what we would infer from the same image in color. Add a hue to black and white, and it stamps its full emotional weight without competition.
In this shot of my daughter, black and white separates her. It shows her alone in her thoughts. We feel her isolation, but that's not the whole story. The warmth of a very gentle sepia restores an intimacy lost in cold whites and grays. We feel her alone only in her thoughts -- not alone in the world.
The same image in color doesn't feel the same way at all. It doesn't feel right. It's little more than a mildly interesting snapshot. It doesn't work.
Black and white is pure. That's why sometimes, it is more vibrant than color.