Much of the information in this answer is adapted from this excellent forum post
In the generic sense
A jackshaft refers to an intermediate shaft that transmits rotation/power from one shaft to another. Per Wikipedia:
A jackshaft, also called a countershaft, is a common mechanical design component used to transfer or synchronize rotational force in a machine. A jackshaft is often just a short stub with supporting bearings on the ends and two pulleys, gears, or cranks attached to it. In general, a jackshaft is any shaft that is used as an intermediary transmitting power from a driving shaft to a driven shaft.
On the 4.0L Cologne SOHC
This particular engine is adapted from an overhead-valvetrain (OHV) design, where a single camshaft actuates pushrods that control valve timing.
As overhead-camshafts make the single camshaft used for the pushrod-engine redundant, designers decided to replace it with a "blank" shaft (jackshaft) that would then transmit rotation from the crankshaft to the rotation via timing chains.
This parts diagram is very useful in describing this rather quirky configuration. The jackshaft is in the middle of the V; the timing chains (Left Hand Front Cassette, Right Hand Rear Cassette) connect it to the camshafts for each bank; the jackshaft is chain-driven off the crankshaft.