“In series” means that one or more heaters preheat water and feed it into a succeeding tank. There are several advantages to this. One is that you don’t have to worry whether the tanks are in balance. In other words, in an in-parallel arrangement, if it is not plumbed properly, one tank may do all the work while the other one just sits there. Even corrosion in the plumbing can throw off what was a well-balanced system.
Another advantage is that the arrangement gives more flexibility. The thermostats can be adjusted to save energy if the entire working capacity of the tanks isn’t quite needed by the situation. And if valved properly so that each tank can be isolated, a complex can continue getting hot water from the remaining tank(s) if one breaks.
The diagram shows cold water entering the righthand tank, being preheated, then sent out that tank’s hot port and into the cold port of the lefthand tank for final heating, then out the lefthand tank’s hot port to the building.