A black body is an ideal physical body that absorbs all incident radiation, regardless of frequency or angle of incidence. Thus, there is no light reflecting from it; for example, Black Holes.
The definition of "Black" is different in Physics from Everyday Life. In Physics, color is a term that anglophones use to describe the various frequencies of electromagnetic radiation, to be more precise, the visible part of electromagnetic spectrum. Therefore, "Black" is not considered as a color in Physics, because the color "Black" is not associated with any frequency of electromagnetic radiation. It causes by, in contrast, the absent of any radiation entering your eyes.
"Blackness in Space" is complicated. Vacuum doesn't mean nothing is there. There is radiation in every part of the universe. You can test this by using your radio and tune it to some random frequency (not stations' frequencies). You will hear the static sound. A small percentage of that sound is coming from outer space (from the Big Bang, to be exact). The technical name of that radiation is called the Cosmic Microwave Background Radiation or CMB. You can't see it because it is in the Microwave region of the electromagnetic spectrum. That is why you can see nothing in deep space, or as most people interpret it, black.
Therefore, if you ask "Does this mean space is black?", it is hard to answer because space, in Physics, has no color due to no visible radiation except for regions of stars. You can't say "space is black" neither because black is not a color.