Systems Integration is the practice of building turn key software and hardware solutions without getting involved in the software development process. Systems integration focuses on productizing a software and hardware solution so that it can be delivered to a 3rd party that has a relatively weak understanding of technology.
A System Integrator (SI) is someone who delivers systems integration solutions for a client using Commercial Off-The Shelf (COTS) software. They are responsible for executing the project, configuring the software, and installing the solution.
An example of a systems integration project would be setting all the hardware and software in a factory that builds cars. Clearly the operators of the plant will have limited knowledge of the software solutions that control the robots and need a turn key solution.