If you are American, then the 'false title' "British explorer and navigator" is regarded as an appositive, identifying the noun "Matthew Flinders" (note the correct spelling of "Matthew').

It is a variation on:
Matthew Flinders, the British explorer and navigator, was...
The omission of the 'the' in your original "British explorer and navigator Matthew Flinders" began with journalists, but has become accepted in the mainstream.

Question 2: is the appositive in this sentence essential or nonessential?

A person has only one father, so this identifies the person. His actual name is interesting, but nonessential.

It should be written:

His father, Auguste Piccard, designed the bathyscaphe.

British explorer and navigator Matthew Finders was the first to chart the coastline.

this sentence is written in my Grammar,usage, and mechanics workbook by holt mcdougel (wrong spelling) there must be an appositive/phrase.. i'm confuced

Mr. Matthews fails to grasp that the omission of the 'the' was a journalistic rendition of 'The British explorer and navigator", and has practice has entered the mainstream. THEY ARE NOW REGARDED AS EQUIVALENT - BOTH ARE ACCEPTABLE.

Totally irrelevant. Appositives by definition are post-head modifiers, i.e. they always follow the noun they modify. So with or without a determiner, the NP "British explorer and navigator" cannot possibly be an appositive in the example that was submitted.

Here are some other examples:

The murderer, the man with the scar, will be arrested soon.
A university lecturer, Dr Brown, was arrested for the crime.
A surprise present, a bouquet of roses, was delivered to my door.

In those three examples, the appositives are in bold, and the NP's they modify are underlined, not the other way round!


PaulM

Hi Zack

No need to be confused!

The appositive in your example is "Matthew Flinders". It modifies the NP "British explorer and navigator".

That is the only possibility.

PaulM