Quote 1
"Pooh – I have as much of mother as father in me!" she said. "All my prettiness comes from her, and she was only a dairymaid." (16.7)
Tess is rejecting her patrilineal inheritance – the noble lineage passed down from her father's side, in favor of her matrilineal inheritance from her mother.
Quote 2
"Londoners will drink it at their breakfasts to-morrow, won't they? […] Noble men and noble women, ambassadors and centurions, ladies and tradeswomen, and babies who have never seen a cow. […] Who don't know anything of us, and where it comes from; or think how we two drove miles across the moor to-night in the rain that it might reach 'em in time?" (30.22-25)
As Tess and Angel unload the milk to send on the train to the London market, Tess muses on the journey the milk is about to take. Critics call the huge gap between those that consume the milk and those that produce it "alienation." It's one of the by-products of industrialization and urbanization. People move to cities to work in factories and have no idea where their milk (or any other food) comes from. And the things they produce in the factories (fancy clothing, for example), gets sold to wealthy men and women who have no idea where the clothing came from, or under what conditions it was made: alienation. Congratulations, you just learned one of the basic tenets of Marxist thought. And it's something that Tess seems to understand instinctively.
Quote 3
From the whole extent of the invisible vale came a multitudinous intonation; it forced upon their fancy that a great city lay below them, and that the murmur was the vociferation of the populace.
"It seems like tens of thousands of them," said Tess; "holding public meetings in their market-places, arguing, preaching, quarrelling, sobbing, groaning, praying, and cursing." (32.4-5)
Here, their imagination makes it seem to Tess and to Angel that the great city is somehow overlaying the peaceful countryside. A trick of the noise made by the rivers and streams make Tess imagine the bustle of the city – thousands of human lives, all going through the various overwhelming assortment of human emotions and activities.
Quote 4
"I'll always be ugly now, because Angel is not here, and I have nobody to take care of me. My husband that is gone away, and never will love me any more; but I love him just the same, and hate all other men, and like to make 'em think scornful o' me!" (42.5)
Angel might have left her, but Tess remains fiercely loyal to him to the point of making herself ugly so that other men won't admire her good looks. Her idea of marriage seems to be that no other men should even look at her if she can help it. But really, her decision to make herself ugly is a practical one – she was getting harassed on the road.
Quote 5
"Why didn't you tell me there was danger? Why didn't you warn me? Ladies know what to guard against, because they read novels that tell them of these tricks; but I never had the chance of discovering in that way, and you did not help me!" (12.81)
What's interesting about Tess's complaint to her mother is what she assumes about the purpose of reading novels. After all, we're reading a novel right now. What does Hardy want us to get out of it? Are we just supposed to learn what "tricks" to "guard against"? Perhaps this passage is partly a defense against those contemporary critics who accused Tess of the D'Urbervilles of being immoral – Hardy seems to suggest that reading novels, even novels with sex parts, is important for women, because too much innocence can be dangerous, like it was for Tess.