When Oblonsky and Levin arrive at the restaurant, everyone knows Oblonsky and is happy to see him, wait staff included.
The waiter fawns over Oblonsky and Levin, and Oblonsky goes through a complicated process of ordering a huge meal: oysters, vegetable soup, turbot, roast beef, stewed fruit, and lots of alcohol.
Oblonsky orders in plain Russian, without using the fancy French that their waiter normally uses. (French is trendy at the moment, and is used everywhere in high Russian society. The name of the restaurant, Angleterre, means "England" in French.)
The situation is uncomfortable for Levin, who would be fine eating bread and cheese.
Levin doesn't want to talk about his love for Kitty in a restaurant he doesn't like. He's afraid the bad vibes of the restaurant will give the relationship bad karma.
Instead, Levin talks about how the city (Moscow) and how the ways people behave in the city make him uncomfortable.
Finally the two men start talking, in a roundabout way, about why Levin has come to Moscow.
Oblonsky tells Levin that his wife, Dolly, has foresight about marriages, and that she likes Levin. Dolly thinks that Levin will marry Kitty.
Levin is excited at this piece of news, but he reveals that he has a terrible inner turmoil. He mentions undisclosed "past sins" and doesn't feel pure enough for a nice girl like Kitty.