Internal labour market refers to the administrative system within a company which determines the internal allocation and pricing of labour.
In the internal labour market, the competition for vacant roles within the company is limited to the pool of labour that is already part of the company. People from outside the company are not allowed to compete for vacant positions.
So a company with an internal labour market that is looking to fill a senior management role, for instance, will look to hire people who have already performed in junior roles within the company. This is in contrast to the external labour market where anyone is free to apply and get chosen for a position.