This is the 11062nd most frequent Russian word.
главному
"Главному" means "to the main" or "to the chief" in English, depending on context.
Here, 'главному' is the dative case of 'главный', describing the engineer.
Главному инженеру поручили новый проект.
The main engineer was assigned a new project.
In this sentence, 'главному' is used to indicate the most important aspect in the dative case.
Она всегда уделяет внимание самому главному.
She always pays attention to the most important.
'Главному' is used adjectivally to describe the type of entrance, in the dative case.