They smith the black metals (iron) as opposed to white(tin), silver(flatwear and other objects), gold(jewelry). It comes from the color of the final product.
I'm going to break this down into the etymology of the word.
Black-a color, and I'm going to come back to this one.
Smith-from the Old English term smythe meaning "to strike"; or potentially from smithaz, a Proto-German term meaning "skilled worker"
But why blacksmith? Iron, the typical material of blacksmiths everywhere, is not black.
The name involves some basic chemistry. When iron is heated in the air, it always lets off a byproduct of iron(II) oxide. This oxide creates a black layer on the metal and thus the term "black".
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