Mitch Hedberg was a stand-up comedian, as opposed to a theatrical or film comic. As we know, in this style of comedy a performer stands in front of an audience and speaks to them, trying to make them laugh. The reaction of the audience is crucial to the act or routine succeeding and proceeding, and the preferred reaction is a constant stream of laughter, punctuated by applause and small amounts of silent attention. To accomplish this goal, and because every comic is suited to a particular kind of delivery, many different styles of stand-up comedy have evolved.
Mitch was in many ways a classic one-liner type of comedian. His routine consisted of very short jokes, most without any kind of set-up or introduction. A good contrast is with the comedy of George Carlin. Some of Carlin's set pieces were several minutes long, structured around a theme, and were built on a narrative, telling a story.
Hedberg's jerky delivery style (he rarely used contractions) was based on quickly spoken jokes and observations, with no thread of connection or narrative between them other than himself. He was not in motion constantly like many comics are, preferring to stand in one place or occasionally sit. Sometimes even turning his back on the audience. He also had certain quirky habits that he worked into his act, such as commenting as if from a third-person point of view on how a joke went over, how the night was going, and so on, with an endearing little chuckle.
His comedy was very different from other popular comics in other ways too. He did not do any political commentary or jokes about celebrities or public figures...it was more "observational humor." His comedy routines were generally not raunchy in subject matter, although he often used profanity when he was able to do so. His many appearances on Letterman give a good overview of his humor, which was very effective without the profanity he could use in clubs.
Finally, watching or listening to a Mitch Hedberg routine gives very little sense of the person inside - we don't learn much about him as a human being. You get the feeling that he is a very private person, and in fact is somewhat uncomfortable up there on stage. He was notorious for having severe stage fright, wearing sunglasses to avoid eye contact with the audience, but he also clearly enjoyed doing a good job of making people laugh,something he was very good at doing.