How do Mr. Bingley and Jane Bennett in Jane Austen's, Pride and Prejudice, help illuminate the relationship between Mr. Darcy and Elizabeth...

The relationship between Mr. Bingley and Jane Bennet in
Jane Austen's novel Pride and Prejudice is meant to represent an
inverse reflection (known as a foil) of the dynamics that take place between Darcy and
Elizabeth. A foil, in literature, is defined as any sub-character (or secondary
character) that is used to contrast the main character (or an idea meant to contrast the
main idea).

You asked how a (secondary) pair of characters
help highlight the main characters of the story. The answer is that Austen, and many
other authors, utilize the foil technique as a way to allow the reader to contrast the
two situations and, in an sort of interactive way, come up with solutions, conclusions,
and comparisons that may help solve the central problem of the
story.

In all, these techniques are also effective in
establishing a strong bond between the reader and the author. It always works well.
Therefore, to concisely answer your question, the way in which one character highlights
another is by foiling it.

To illustrate this explanation,
think of how Jane and Bingley seem to be quite alike: Both are a bit shy, sympathetic to
everybody, and none of them have the gall to take the first step in declaring love for
each other. In fact, their relationship is so passive that even Charlotte Lucas wonders
when "anything official" would take place. Similarly, Mr. Bennet judges them to be so
complaisant with everything that he feared that they will end up failing in the
financial sector. What Mr. Bennet basically declares is that, to him, Jane and Bingley
are so alike (and sort of airheaded) that he worries about
them.

In a huge contrast, we find Austen clearly focusing
on the relationship between Darcy and Lizzie. They are both passionate and sort of
enigmatic. He is proud, aristocratic, and  prude. She is prejudiced, independent, and an
outspoken smart-mouthed girl. Both hate each other, both love each other, both get
confused with each other....it is a roller coaster with Darcy and Elizabeth. And, yet,
everything gets fixed happily in the end.

However, it would
have not been as effective to show the one sided aspect of Darcy and Elizabeth without
first presenting us with the story of Jane and Bingley. Just as we have had enough
glurge with those two, the action begins: We see the darker side of the love moon in
Lizzy and Darcy.

Conclusively, the use of a foul to
highlight the unique characteristics of the main character of a story is an effective
method to bring the reader closer to the main character. It allows the reader to
compare, contrast, and create connections to the story. That is always a positive thing
in literature.