In respect to this, what does country of issue mean on passport?
'Country of issue' refers to the country in which the passport was issued to you. In case of a passport being issued by the (Dutch) embassy in London the country of issue will be 'United Kingdom', and under 'nationality' you fill in 'Dutch'.
Beside above, what is country or territory of issue? Your "Country of Issue" is the same as your "Country of Citizenship". For instance, if you are a citizen of the United Kingdom, but are getting your passport from the UK Consulate in Hong Kong, the UK is your country of issue.
Consequently, how do I know the country of issue of my passport?
The first concept is "country of citizenship" and the second is "passport issued at." The country of your citizenship is the issuing country - it doesn't matter where it's issued.
Where is the place of issue on a UK passport?
There is no specific "Place of Issue" on the British passport, although there is "Authority", which says IPS or Passport Agency depending on when your passport has been issued. IPS was the name used for the issuing agency before it was changed to HM Passport Office (HMPO)..