Actually I am reading a paper for school homework. This paper is called : "JASPER: Joint Optimization of Scaling, Placement, and Routing of Virtual Network Services". They use the term "substrate network". So I am confused about that term term , I hope someone can explain what is its meaning.

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You seem to be talking about https://ieeexplore.ieee.org/document/8382313. I haven't read the document, but it's mentioned in the abstract:

In this paper, we propose joint optimization of scaling, placement, and routing (JASPER), a fully automated approach to jointly optimizing scaling, placement, and routing for complex network services, consisting of multiple (virtualized) components. JASPER handles multiple network services that share the same substrate network; services can be dynamically added or removed and dynamic workload changes are handled. Our approach lets service designers specify their services on a high level of abstraction using service templates.

So what they're describing is a way of building network services on top of one underlying network, which they call the substrate network. It mostly sounds like another description of NFV (Network Function Virtualization), where the actual network functions are abstracted and separated from underlying infrastructure.

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