The verb stem + なさい - nasai is a command (* 3).
It has a strong implication that you are "talking down" to somebody, or that you are more mature, know better, and should be obeyed. 
なさい, therefore is appropriate for parents to use toward their children or for teachers toward their students.

You also often see nasai in exam instructions.

uchi-ni mainichi denwa shinasai.

Fill in the blanks with a word.
"Inside the brackets, word enter-please."

* 3

nasai goes directly on a verb stem, and therefore it can only be used for commands in the affirmative.
To issue a command in the negative, you can use the te-form + wa ikemasen, which we learned in
Lesson 6.