A closed instance represents a single completed or terminated flow of a process. It is the opposite of an open instance, that is a running, unfinished one. And if the applied methodology or app of process management allows for it, it is usually possible to re-open an already closed instance and continue.
I know, I know, too abstract and complicated. Let’s play with an example here. Let’s say we have a process to manage orders in a cabinetmaker’s shop, where every instance usually represents a particular product or commission: a set of chairs, a wardrobe, a dining table, a garage bookcase, an oak coffin, etc. A closed instance would represent either 1) a commission, that was properly finished and delivered, or 2) an order, which wasn’t successfully finished for some reason — for example because the customer bought bitcoins instead and canceled the order for some chairs, or kicked the bucket before he paid in cash for the coffin. Too bad both for him and the cabinetmaker!
In any case it is always good to keep records of all closed instances, because the stored information might prove useful to the owner (and the whole cabinetmaker’s shop) in the future and possibly serve as a basis for a deeper analysis some day.