Payments and securities trading are the classic examples: a trade or a payment instruction moves from initiation to settlement without a person retyping details into another system at any stage, which cuts processing time from days to minutes and removes a source of manual entry errors.
Full straight-through processing is hard to reach outside well-standardized, high-volume flows, since it requires every system in the chain to accept the transaction automatically. Most businesses land somewhere in between: the standard case goes straight through, and exception handling catches the transactions that do not fit the standard pattern for a person to finish by hand.