On a shared architecture like the Origin2000, each processor has memory associated with it. For a large job using many processors, data will reside in the memory where it was first assigned, on any one of the processors. But the controller has a map of what data is where, so any processor has access to any piece of data. How far away that data is depends on the topology of the interconnections, and distant data means a performance hit.
On a distributed memory machine, data resides with the various processors again. We as programmers must send data where it is needed, by either processor to processor messages or by broadcasting a message. Which you do has implications in performance.