The specialist is someone you can employ in your company. He/She is a bit more expensive than a 'generic' employee. However, it's someone with skills that affect certain aspects of the game depending on their assigned job. There are 3 different jobs you can assign a specialist to. Director, Secretary and Employee. Increasing your management skill will allow you to hire more specialists.
Each branch in your business can have 1 director. The director is the manager of the branch. His main skill is 'Management'. The higher his management, the more he will increase production in the branch. He also still affects the productivity like a normal employee on top of that. However, being director he will increase his Management skill and not the skill relevant to the branch.
A secretary is similar to a director in that there can be only 1 secretary for each branch in your company. However, the main skill of the secretary is 'administration'. He/She will level administration while assigned to be the branch secretary. The total skill of all your secretaries and yourself combined in 'administration' will increase the 'contracts' wich you can sign. So, if you are at the contract limit, hire a capable secretary.
A higher contract limit will also draw in more 'customer funds' for banks.
The employee is mainly there to help out generic employees in increasing their productivity. Where a 'generic' employee increases production by 1, a 'specialist' employee will greatly boost production depending on his skill level in the skill relevant to the branch. However, assign only 1 specialist employee for each 1,000 generic employees, or they'll start bothering eachother and the effect will be gone.