In "Sir Gawain and the Green Knight," what does the opening, about nation-building, have to do with the rest of the poem?

If you read the beginning of the preface to Gawain's tale,
you will note that the narrator begins his story in the past, laying the ground work of
events that transpire before Arthur's time.

Not only does
this provide the story with roots, but it makes it seem more plausible as the narrator
gives a credible history as to how the world arrives at a place where Arthur and his
many adventures take place. By giving a history, it makes the story more
plausible.

For example, if a story is written where a
magical kingdom appears from nowhere, the reader has a sense he is reading a fairytale.
However, if a story is written with a sense of history, the stories are more believable.
(Giving the history does not make the Arthurian legends true, per se, but lends a sense
of authenticity to the stories).

To add a sense of reality
to the tale, the narrator starts with the famous battle of Troy, between the Greeks and
Trojans. This famous battle is believed to have actually taken place. Providing
information about this widely-accepted occurrence in history also provides a sense of
realism.  It gives one the feeling that the information to follow is based on fact.  The
narrator describes the war's aftermath—how the world begins to rebuild after the
hostilities that went on for so many years.

The
introduction to the story tells of the reconstruction of civilization: including the
building of major cities such as Rome, Tuscany, and ultimately Britain. The description
of the founding of the kingdom of Britain provides the pathway through the generations
that leads up to the birth of Arthur, and, later, his place in history as the greatest
of all British Kings. For years, many people believed the stories of Arthur's heroic and
honorable feats.

Providing a history of how his country and
he came to exist, makes the stories more believable. There are, of course, indications
that Arthur did, in fact, exist, but that he lived long before the
medieval period, so he would have been dressed in skins rather than armor— but he was
still an excellent warrior, highly admired by his
people.

Any time we try to make something real, whether a
character in a story, or even find the certainty that an event took place, the act of
including history of some kind gives credibility to the person or event by looking back
to history for its beginnings.