what is the purpose of the Board of Trustees for charter school their duty. why aren't traditional public school govern by a board of trustees.

Typically, a Board of Trustees for a charter school is meant to provide leadership for the school.  It is a level above the principal that would set goals for the school and do other sort of strategic types of thinking.

The reason that regular public schools are not governed by these types of boards is that they are already governed by various other boards.  Typically, public schools are governed by an administrative office.  Where I live, this is called the office of the superintendent.  The office of the superintendent is responsible for setting the overall goals and strategies for the school district.

Charter schools are meant to be outside this system so they can do their own thing, but they still need some administration.