auxiliary verb
Light imperative auxiliary verb attached to the -masu stem of a verb. Used toward someone of equal or lower standing, such as a parent to a child or a teacher to a student. Softer than a direct imperative but still a command.
See also: なさる
早く食べなさい。
Eat quickly.
ここに名前を書きなさい。
Write your name here.
Hurry up and tidy this up!
ください is a polite request form usable with anyone, while なさい is a plainer command typically used by a superior toward an inferior, such as a parent to a child.
なさい is the standard, nationwide polite imperative ending, whereas りん is a softer imperative used only in the Mikawa dialect.
な is the blunt, casual abbreviation used with the -masu stem, while なさい is the fuller, more polite imperative form it comes from.
なさる is the honorific dictionary-form verb meaning 'to do', while なさい is its imperative form used as a light command auxiliary, so learners often confuse the two.
Imperative form of the honorific verb なさる, which itself is derived from 為す (なす, 'to do') with the honorific auxiliary る.