It's all about Data Flow. In a Serial arrangement, Routine 2 cannot begin to run until Routine 1 finishes (and sends its data to Routine 2), and Routine 3 cannot begin to run until Routine 2 finishes. Let's say Routine 1 takes 1 second, Routine 2 takes 2 seconds, and Routine 3 takes 3 seconds -- the Serial sequence takes 6 seconds.
When routines run in Parallel, the CPU time is "shared" between them. There is no "predictability" to the order that code is executed -- in particular, you cannot predict which one finishes first, second or third. If Routine 1 takes 1 second, Routine 2 takes 2, and Routine 3 takes 3, doing all three in parallel will take a minimum of 3 seconds (and, in many cases if the routines are not "compute-bound", they might all finish in 3 seconds, too, as Routine 3 can run while Routine 1 is "idle" (say, waiting for a File to open). The three routines share the CPU, with cycles allocated according to some internal scheduling algorithm.
This makes LabVIEW an inherently parallel programming language.