System integration involves joining existing disparate services or systems together into a single view or process for the user.
Good examples of this are the personal banking sites which allow you to access their 'back-office' systems which contain your banking information.
With system integration your business offers a much greater 'value added' service to to your customers by providing them with all the information they need in one place and in one process, instead of having to use a number of different systems.
By using system integration you greatly improve user experience and effectiveness of the business process.
E-commerce websites typically integrate with a number of different 'back-office' systems which handle such as ordering, processing, tracking and payment systems.