Basicially, a "slightly spicy" to "flaming hot" sausage made of beef and pork. It is analogus to the Hillshire Farm® brand Link Sausages. The sizes can vary from "long Polish" to hot dog size.
Half-smokes are a phenomenon known locally to the Washington Metro Region, (DC, MD, VA).
I also know half-smokes as "somewhat spicy smoked sausage(s), usually made of pork and beef." But, I know them as very small about half the size of a normal breakfast link, (which would make it a horrible nickname).