A cyclic haulage system refers to one that uses "load-haul-dump" cycles. Classic truck and shovel operations are an example of cyclic haulage. After material is either blasted or dug by the shovel, the shovel picks up the material, loads into trucks, and the trucks transport material to another location.
A continuous haulage system refers to one that uses conveyors or slurry pumping to move material from one point to another. For conveyor haulage, some sort of machine is still need to load the material onto the belt, but trucks or other cyclic haulage equipment can be eliminated.
Both types of haulage systems have pros and cons, depending on the mining operation logistics and needs.
Figure: Cyclic hauling can be seen in the first image, while continuous hauling with a conveyor can be seen in the second image.