In Part 2, Chapter 25, there's a major turning point in the novel: Vronsky goes riding on a steeplechase in competition with a bunch of other men in his regiment. His horse Frou-Frou (who Vronsky calls "sweetheart" and "lovely") is a high-spirited young mare, eager to get out there into the mix and show those other horses what's what. But as Vronsky's riding, he makes a mistake that trips up Frou-Frou. She falls and breaks her back while he manages to escape uninjured. Now, in terms of the plot, what's important about this scene is that Anna and Karenin are both attending the race, and Anna's visible concern at Vronsky's fall tips off Karenin, at last, that she really is having an affair.
What's important about the scene symbolically is that it foreshadows what's going to happen to Anna herself. Vronsky is absolutely taken with the horse, but his love of her doesn't prevent him from doing something that ruins her forever – he misjudges where he's put his weight as Frou-Frou is gearing up to jump, and she breaks her back. This is similar to his relationship with Anna. Vronsky loves Anna, but he convinces her to have an affair with him, which destroys her. Vronsky's great tragic flaw is that he's capable of deep love, but he's just not that careful, and his lack of care has terrible consequences for the women (or female horses) with whom he gets involved.