When analyzing sociological background, one is analyzing the type of society that the author is writing about. You are analyzing things like the types of government, types of laws, and types of rules. You can also analyze if you think the author actually likes the society, or does he/she dislike it. This can also lead you to analyze what social changes the author might make.

Jane Austen's Pride and Prejudice is a very true sociological reflection of Austen's own social situation during the Regency period. Just as Austen knew it, England's government in Pride and Prejudice is a monarchy that is governed upon the advise of the Prime Minister, Cabinet, and members of Parliament. Also, just as Austen new it, her novel's society is divided by class rank, including the noble class, the landed gentry, the middle class, and the merchant class. In fact, one social phenomenon Austen experienced herself and wrote about in the book was the increase in wealth of the merchant class. Around the same time as the French Revolution, some members of the merchant class were becoming increasingly wealth, wealthy enough to rub shoulders with the landed gentry, purchase estates of their own, and live among the gentry. At the same time, the English nobility watched all of the French nobility be beheaded. Not wanting the same fate, the English nobility decided to begin softening some of the lines of demarcation separating classes. Austen's era began seeing the intermarrying of the classes ("Social Evolution"). Both the rise of the merchant class and the mingling of the classes are social issues Austen covers in her novel.

Austen especially portrays the social issue of the rising merchant class with Mr. Bingley. Austen makes it evident that Bingley's father actually earned the Bingley fortune through trade and left it to Bingley to buy the family estate. However, using Mr. Bingley and his sisters, Austen points out the consequence from the social phenomenon, which was in increase in prejudicial snobbery. In particular, we see Bingley's sisters criticize the Bennet family, which are actually in a class higher than they are since Mr. Bennet is gentleman with an estate, simply because Mrs. Bennet is descended of the working class, just like the Bingleys. As Austen phrases it:

[The Bingley sisters] were ... in every respect entitled to think well of themselves, and meanly of others. They were of a respectable family north of England; a circumstance more deeply impressed on their memories than that their brother's fortune and their own had been acquired by trade. (Ch. 4)

Hence, one aspect of society Austen shows a desire to change is class snobbery.

In addition, Austen also portrays inter-class marriages when she has Elizabeth marry Mr. Darcy. Technically, they are members of the same class. As Elizabeth points out to Lady Catherine de Bourgh, "In marrying your nephew, I should not consider myself as quitting that sphere. He is a gentleman; I am a gentleman's daughter; so far we are equal" (Ch. 56). However, some, like Lady Catherine, may consider Darcy to be a cut above Elizabeth because he has noble class relations while Elizabeth, again, has working class relations. Austen is not only using the marriage of Elizabeth and Darcy to support inter-class marriages, which were on the rise in her society, she is also using Lady Catherine to once again criticize class snobbery.

What is the context (historical, cultural, social, political) of Jane Austen's Pride and Prejudice?

Hope this helps:

Historical and political context: The setting takes place around the late 1700's and early 1800's during the Regency period. Regency means that England was not ruled by a King or Queen, but by a Prince Regent, in this case it was the son of the (mad) King George III, Prince George Regent who would eventually become King George IV.

In France, the Napoleonic Wars were going on, and Marie Antoinette, and the entire French aristocracy had been beheaded or exiled, causing much commotion in England while solidifying the snob-factor of the English upper classes. In other words, it was as if what happened in France made the English rejoice so much (they have long hated each other) and made the English go all out. Plus, the Prince Regen avidly supported social separation as he himself was a first class spendrift.

Cultural and Social context: During Prince George's regency there was not much order as he was a very unsympathetic lusty and ridiculously unintelligent man. Class division basically took a personality of its own and it was more divided than every. Gender was clear issue and women were still treated as second class citizen despite of rank. Social mobility was completely obstaculized by prejudice of rank, birth, and status. Women would never attempt to gain ownership of anything except through marriage. When married, women become a PART of the household whose function is to moderate all the other parts.

The job of females, then, is to produce children but even during this Regency male heirs, whether rich or not, were given first priority. This is why the character if Mr. Collins is the heir to the Bennets estate.

Hope this helps a bit!

What contexts and values of her times does Jane Austen examine in Pride and Prejudice?

Some contexts of her time that Jane Austen examines in Pride and Prejudice are the military, farm laborers, and estate wills. Austen is unique in that she does not discuss externals directly, either in terms of descriptions or social contexts. She does however allude to or indirectly infer some. The presence of the Regiment in Meryton alludes to England's military involvements. Pride and Prejudice was written between 1796 and 1798. In most immediate proximity to the writing period, England signed a treaty in 1795,, which was ratified in 1797, with the United States guaranteeing that England would remove its regiments from the US Northwest territory. In 1796, General Bonaparte led the victory against Austria; though England was not involved, this was nonetheless part of the military context of the times.

Regarding farm laborers, when Elizabeth visits Rosings, it is made quite clear that Lady de Bourgh takes an active interest in overseeing the running of her estate and the lives of her farm laborers. Darcy's housekeeper alludes to the same overseership of farm laborers when she says,

"He is the best landlord, and the best master," said [Mrs. Reynolds], "... There is not one of his tenants or servants but what will give him a good name."

Property laws, and particularly entailment of estates away from the female line, are alluded to through the presence and role of Mr. Collins, who would have married one of the Bennet girls in order to keep the property in the Bennet family.

Values that Austen examines are contained with her themes: love and marriage; pride and prejudice; wealth and prestige; middle class wealth. Love and marriage are examined through every major character from the ill-behaved, scandalous Lydia, Wickham and Mrs. Younge to the practical and ridiculous Charlotte and Mr. Collins to the proud and prejudiced Elizabeth and Mr. Darcy. For example, Austen examines the necessary link between love, marriage and society when Colonel Fitzwilliam informs Elizabeth that his position in life depends upon his marrying a wealthy upper class woman because he is a penniless earl’s second son who, as such, cannot inherit lands, title, or wealth. Austen examines the relationship between love, social standing, independence, and marriage through Charlotte's decision to marry Collins for independence and position without any love being involved--good will stands in the stead of love in Charlotte's attachment to Collins.

Wealth and prestige follow the examination of love and marriage in Austen's novel. The issue enters  into every relationship and problem. For example, Bingley is worthy of a marriage with a gentleman's daughter because his father was successful enough at a trade to be significant wealthy to give his children lives of privileged independence. He thus came to represent the newly risen wealthy middle class. The Gardiners further represent the connection between wealth and prestige. Gardiner is a tradesman; Elizabeth scorns to think of Darcy or the Bingleys enduring a relationship with such an individual:

Mr. Gardiner was a sensible, gentlemanlike man, ... [They] would have had difficulty in believing that a man who lived by trade, and within view of his own warehouses, could have been so well-bred and agreeable.

Yet, after Darcy's change in inner character, it is with Gardiner's help that he rescues Lydia, thus emphasizing a newly begun re-evaluation of wealth and social prestige.