As others have stated, it's an engraving. Which is a physical technique first and foremost (and, of course, later adopted as a style for non-engraving situations).
Engraving works by etching or carving away the surface of a (typically metal) plate. The ink is trapped in these recessed areas, and that is in turn applied to the paper. This is why engraved printing, such as US Currency, has a raised feel to the ink.
With engraving, the positive parts of the image are what are carved away from the printing substrate. This is opposed to wood cut or lino cut art, where you carve away the negative parts of the image.
As for 'era' this was widespread pre and turn of the century. One place to obtain copious amounts of stock art in this style are the Dover Stock Art books.
The technology and technique of engraving predates the 1900s by a few centuries (originating in roughly 1400s Germany) but in terms of contemporary graphic design, it definitely tends to have a 'turn of the century' feel given that it was in almost universal use for mass produced printing (such as catalogs and newspapers and the like) which correlated to the start of the consumer-driven era (hence a lot of art was created to "sell stuff") and a massive amount of it was produced during that era, much of which was later collected and compiled into stock art collections such as the aforementioned Dover which gave the art and style a prolonged life.