Children born out uk from british overseas parents

I need some information about what should i do to get a british overseas citizen passport for my children

British overseas citizen is a specific sub section of the nationality law and has limitations on living in the UK.

What is the exact status of the parents and how did they obtain it?

As CR001 has mentioned above, "British Overseas Citizen" has a specific meaning in law and does not mean British citizens living abroad.

Are either parent of the children a "British Citizen" living abroad or are they "British Overseas Citizen"? Their specific status (whether they are a "British Citizen" or a "British Overseas Citizen") will be listed in their (the parent's) British passport.