An integration links separate pieces of software so they share data automatically. A common example is a booking system that creates an invoice in the accounts package, or a website form that creates a record in the customer system. Nobody has to copy anything across.
Without integration, staff copy information between tools by hand, which is slow and invites mistakes. With it, each fact is entered once. Integrations can be direct, through an API, or handled by an automation tool in the middle. They need looking after, because when either side changes, the connection may need adjusting.