the determination of your product system is part of the Goal&Scope of a LCA. Usually, you have a certain objective when conducting a LCA, e.g. you want to compare the function of two products or services. Let´s say we want to know the ecological impacts of tissues that will serve the function of drying our hands.
Referring to the ISO definition you have already mentioned, the product system collects all processes that are needed to perform this function. For tissues, this could include tree planting and wood production, followed by paper production, use and waste treatment - and transport of course. All these processes form your product system here. In the perfect case, the input and output to your system are only elementary flows (see ISO) and one product flow, but as this is not feasible in reality, insignificant by-products and preliminary products will cross the system boundaries. For example, when thinking of transportation, there might be rail trannsport. It is now necessary to think about how far you want to expand your system (starting at the obvious processes over the life cycle that I mentioned before), e.g. if the construction of the railway must be part of the product system, too. Usually, it isn´t and you´ll and leave infrastructure out of your system boundaries.
Hope this helps you.