A website on its own is just pages. The moment it needs to take a payment, accept a booking, add someone to a mailing list, or push an enquiry into your CRM, it has to talk to another system. That connecting work is integration, and it's what turns the website into part of how the business runs.
Done badly, or not at all, it leaves gaps that get filled by hand: enquiries copied from an inbox into a spreadsheet, bookings re-keyed into a calendar, customer details typed into a CRM after the fact. Every one of those gaps is slow, and every one is a chance to make a mistake.
Done well, the systems talk to each other directly. A booking made on the site appears in the calendar. A new customer lands in the CRM. A sale is recorded, a confirmation email goes out, the numbers reach the right place, and nobody has copied anything anywhere. The website becomes part of how the business runs, rather than a separate thing to keep in sync.