i know what this means.. but what is the origin of しなさい ?
Does it come from する (to do verb) ??
Is it short form of something? or what?
しなさい is a verb conjugation that turns the verb する into a command (imperative form). There are a number of imperative forms, but this one in particular gives the nuance of "talking down" or giving advice that you feel is helpful to the listener (but keep in mind, it carries the connotation that you know better than the listener). This is generally how a parent would speak to his or her child, or a teacher would talk to students.
If you're not sure whether or not it's appropriate to use in a given situation, imagine saying it in English with the phrase "You had better". e.g:
The ーし part comes from する, indeed. It is the infinitive form, or what some grammarians like Seiichi Makino call the "masu stem": the form of the verb that takes －ます.
する → し → します
なさい is the imperative form of なさる, which is a honorific word which means the same as する.
Infinitives combine with なさい to form firm, but polite orders.
For instance, telling children to sit down:
座る → 座り（ます） → 座りなさい （すわりなさい）
Or encourage them to eat:
食べる → 食べます → 食べなさい
The し arises when the verb is any one of those formed by -する, or anything else whose masu form ends in し. For instance, 押す → 押し（ます）
Here, definitely there is no しなさい as a unit; since 押し is a unit!
You have probably heard しなさい by itself, though (when し is from する):
あなたも、そうしなさい。 (You too, do the same!)