Internal customer service involves multiple departments within a business coordinating together to achieve the aims of the company.
For example, the recruitment process isn’t just a job for one employee or even one department. Someone will be responsible for advertising the job, another for screening and interviewing candidates at a service desk. HR will then on-board the successful candidate and provide orientation. The accounts department will then enter them into the system so that they can be paid. You may also involve the IT department or other industry experts who must ensure the new employee has the equipment they need all set-up and ready to go on their first day.
This requires a lot of cross-team communication and inter-departmental teamwork, all of which falls under the umbrella of internal customer service.