Apache NiFi handles data from many disparate sources and can route it through a number of different processors. Let's use the following example (ignore the processor types, just focus on the titles):
First, the relative rate of incoming data can be different depending on the source/ingestion point. In this case, the database poll is being done once per minute, while the HTTP poll is every 5 seconds, and the file tailing is every second. So even if a database record is 59 seconds "older" than another, if they are captured in the same execution of the processor, they will enter NiFi at the same time and the flowfile(s) (depending on splitting) will have the same origin time.
If some data coming into the system "is dirty", it gets routed to a processor which "cleans" it. This processor takes 3 seconds to execute.
If both the clean relationship and the success relationship from "Clean Data" went directly to "Process Data", you wouldn't be able to control the order that those flowfiles were processed. However, because there is a funnel that merges those queues, you can choose a prioritizer on the queued queue, and control that order. Do you want the first flowfile to enter that queue processed first, or do you want flowfiles that entered NiFi earlier to be processed first, even if they entered this specific queue after a newer flowfile?
This is a contrived example, but you can apply this to disaster recovery situations where some data was missed for a time window and is now being recovered, or a flow that processes time-sensitive data and the insights aren't valid after a certain period of time has passed. If using backpressure or getting data in large (slow) batches, you can see how in some cases, oldest first is less valuable and vice versa.