Haymitch is a former District 12 tribute and winner of the Hunger Games who is now a middle-aged drunk. His job is to come out of his alcoholic stupor long enough to coach Katniss and Peeta to victory in the Hunger Games. (Ha.) He tends to use condescending names like "sweetheart," which does nothing to endear him to the sometimes-haughty Katniss.
Despite his shortcomings, Haymitch serves as a very human and intermittently likable mentor figure for Katniss and Peeta. He coaches the pair from a position of experience: he understands the rules of the Hunger Games and the celebrity culture surrounding it. Haymitch knows the importance of creating a persona, and encourages Katniss to go along with the romance plot introduced by Peeta. After all, as Haymitch says: "Who cares? It's all a big show. It's all how you're perceived" (10.24).
Whether Katniss wants to admit it or not, she and Haymitch are actually very much alike. Like Katniss, Haymitch is smart – when he's sober. The two are certainly survivors, a point proved by Haymitch's former triumph in the Hunger Games of long ago. Because of this connection, they are able to communicate during the Games through the sponsor gifts that Haymitch sends, such as in the pot of broth in Chapter 19:
Haymitch couldn't be sending me a clearer message. One kiss equals one pot of broth. I can almost hear his snarl. "You're supposed to be in love, sweetheart. The boy's dying. Give me something I can work with!" (19.92)
As a now troubled victor, Haymitch is also a reminder that perhaps no one ever really wins the Hunger Games. After all, Haymitch's lonely life consists of the very depressing task of coaching tributes – and usually watching them die.