Generally speaking, those who are at lower levels of an organization serve those at higher levels. Bosses boss and their employees serve; coaches devise strategy and players do what the coach tells them to do; engineers design car parts and workers assemble them according to the engineers' instructions. Ideally, of course, it's a two-way street: A good boss knows he is really there to help his employees succeed; a good coach creates strategies based on his players' strengths. Even there, though, the boss and coach are really working in service of a higher goal, seeking organizational success.
The same is true in the spiritual sense of the Bible. When someone serves another, they are in a lower state, serving a higher state (or a deeper evil, if they are being enslaved by those who represent evil). This can take many different forms, depending on the circumstances.
In many cases, this creates a connection between "service" and intellectual things. This is because who we are is determined by what we love; our loves are the deepest part of us. What we think, our reasoning and intellect and the things we learn about, come from those loves and serve those loves.