An integrated system shares data or commands between subsystems, so an access event can pull up the matching camera, or an alarm can lock a door. Integration depth varies: a simple event link is not the same as one platform that configures, monitors and controls every device.
Integration is often sold as a list of logos rather than a working outcome. The question worth asking is what one system will actually do when the other reports something.
What integrates, and how
Common links run over a network API, ONVIF events or a hardware relay. APIs carry the most detail but tie the two systems together across firmware versions.
The work behind the demo
Integrated systems need a shared clock, a documented network, time to test each link, and an owner when something breaks. Those are the parts that fail first.
Related:Glossary: Access control systemGlossary: Video management system