Balance shafts are a technology which were patented by Mitsubishi under the name "Silent shaft technology" in the mid-1970s. Mitsubishi's implementation was first used in 1974 in the original Astron and later licenced to other manufacturers including Porsche and Volvo.
Balance shafts are used to reduce the second-order vibration (vibration that occurs twice per revolution) inherent in some engines. Their most common application is in inline 4 cylinder engines which have this second order vibration due to the fact that the conrods do not move in a symmetrical fashion. Basically, balance shafts are intended to make the engine smoother.
To achieve this balance shafts rotate at twice the speed of the crankshaft. These shafts are fitted with equally sized weights and rotate in opposite directions to each-other (hence the term - counter-balance shafts).
The concept of balance shafts has existed for a long time but it's implementation was difficult. It was difficult to support and lubricate an object rotating at twice the engine's speed. Mitsubishi solved the problems that faced other manufacturers and then patened their solution.
Balance shafts cost the engine some power and reduce it's revability. There seems to be varying claims as to just how much they cost the engine. It is not uncommon for some owners to remove them from their engine to reduce complexity and increase performance. Kits are available to remove them from both the Astron and Sirius engines used in the Magna.