According to bronfenbrenner's ecological systems theory, the refers to the interactions between and among the systems.

Child development  

Explanation:

This theory focused on child development and interaction with the context. The theory indicates the entangled layers of the environment which affect the growth of child development. The name of this theory becomes renowned as a Bio-ecological Theory which suggests that child biology is the primary factor that sustaining his development. The main factors which contribute to the maturing of children are his biology, family environment and social interaction. If some changing occurs in one layer get impact on other layers.  

Bronfenbrenner's gives five layers of the system areas:

d. i assume the underlined word is "role." reformat if it isn't.

explanation:

role is closest to part because when replacing words, "playing a vital decision," "playing a vital activity," and "playing a vital dollar" don't make logical sense. the only meaningful choice is "playing a vital part."

this fits one of merriam-webster's definitions of role: "a function or part performed especially in a particular operation or process."