Example 1: Hardware Integration
Some organization have Electrical Hardware building blocks that have been pre-designed, tested and validated. These building blocks could be for step-down regulator circuits, microcontroller controller circuits, audio processing circuits, video processing circuits, AM/FM RF circuits, BLE circuits, etc. In order to design a product electrical hardware engineers would select the appropriate electrical hardware building blocks and integrated them to create an electrical hardware product.
Example 2: Software Integration
Like the above some organization have software building blocks that have been pre-designed, tested and validated. These software building blocks are pre-designed, tested and validated. These software building blocks are designed to control and process data from electrical circuits similar to the above hardware building block list. A software integration engineer(s) would select the appropriate software building blocks to create a software design that would control the electrical hardware.
Most modern day electrical products require both Hardware and Software. Therefore, combining example 1 Hardware and example 2 software is considered hardware and software integration.
The purpose is to encourage re-use of proven building blocks to reduce product design time thus reduces time to market.