How does Pemberley symbolize Mr. Darcy?

When it comes to describing the characters of Pride and Prejudice, it is easy to connect the characters’ traits to those of their dwellings. After all, the English class system of 1813 was much stricter then than it is now. This means that your surroundings pretty much defined who you were in society. Those who had more financial and social privilege would have made sure to have possessions that would show just that. This is the case with Pemberley.
Pemberley definitely matches its master, Mr. Darcy. First, Mr. Darcy is the wealthiest among his circle of friends in the novel. As such, his home is the largest and fanciest in comparison to Bingley’s and, of course, the Bennet's. Just as his home is beautiful, so too is the man himself. According to the novel,

the gentlemen pronounced him to be a fine figure of a man, the ladies declared he was much handsomer than Mr. Bingley, and he was looked at with great admiration […]

This is another way that Pemberley represents Mr. Darcy. Darcy’s home provokes the admiration of others, again, even more so than Bingley’s Netherfield Park.

Elizabeth […] had never seen a place where nature had done more, or where natural beauty had been so little counteracted by an awkward taste.

Moving to the subject of legacy, let’s remember that Pemberley is not a second home or a temporary dwelling, like Netherfield Park. Pemberley is the estate of Mr. Darcy’s family. It has been in the family for generations. This is an important thing to consider, because it shows that when it comes to social standing, Mr. Darcy is the highest ranking among his friends.

They are descended, on the maternal side, from the same noble line; and, on the father's, from respectable, honourable, and ancient -- though untitled -- families.

From a metaphorical perspective, we can also connect Pemberley to Mr. Darcy’s own personality. He is someone who, like his ancient estate, represents tradition. Notice how hard it is for him to propose to Elizabeth, whose family (mainly, their behavior and lack of decorum) would never match the respectability of his own family. Also, he is very aware of the importance of keeping the family name free from scandal. He even fixes the entire situation with Lydia, Elizabeth’s sister who shamelessly elopes with her lover Wickham.  Darcy normalizes the situation precisely to ensure that his own name does not become tainted by his association, or future association, to the Bennets.
Pemberley House is elegant on the inside, and open for hunting and fishing in its grounds. It is a home that accommodates people. It is a place that represents hospitality, partly because there are plenty of resources to be shared. Similarly, Mr. Darcy proves to be a generous, kind, and fair man in the novel. 
In all, Pemberley is just like Mr. Darcy: unique, worthy of admiration, aristocratic, and a symbol of true wealth.