On the day of the races mentioned in the previous chapter, Vronsky comes a bit earlier than usual to eat lunch in the regimental mess. He's leaning over a French novel, but he's not really reading—he just doesn't want anyone coming up and talking to him.
He's preoccupied (as usual) with thoughts of Anna, who he hasn't seen in three days.
He thinks up an excuse to visit her by saying that Betsy sent him to see if she would be going to the races.
Two officers go over and try to talk to Vronsky about his eating and drinking before the race. They irritate him.
Next, Yashvin, a captain, goes over to Vronsky and is well received, by contrast.
Yashvin is Vronsky's best friend in the regiment. He's also a man who doesn't seem to have any morals. He's described as a gambler and a rake. (A rake is an old-fashioned term for a "player." Yashvin is a player who enjoys breaking ladies' hearts without ever getting tied down.)
Vronsky likes Yashvin for a lot of reasons: he's strong, he's a great drinker, he's got a lot of character, and he can do any number of things with great skill in spite of all his drinking. Most of all, Vronsky believes that Yashvin likes Vronsky for who he really is.
Vronsky also feels that Yashvin would be the only friend he has who could possibly understand his desperate love for Anna.
The two men chat about Yashvin's gambling and Vronsky's chances for winning the steeplechase, and then the two head over to Vronsky's place for a bit of drinking.