To heckle is to challenge or harass someone. At a sporting event, fans sometimes heckle the opposing team, but it’s not very respectable behavior.
One of the many challenges of being a stand-up comedian is dealing with people harassing you from the audience. Those people are heckling. While heckling in a comedy club is not all that unusual, it’s still rude. If you choose to heckle someone, whether they are a comic or anyone else, be prepared to be heckled back — or worse.