As you move across a special mat at the starting line, the chip registers that you've started the race. Then, as you cross the finishing line, the chip registers that you've finished the race. So, in other words, the amount of time that it takes you to reach the starting line (since most people are not right at the front of the race) doesn't count in your overall time. In some cases of very large races, it can take runners at least 20 minutes to reach the starting line. Your chip time is different than your "gun time," which is the amount of time it took you to finish the race from the moment the gun (or horn) went off.
Most large races, especially marathons, now use chip timing technology. As a result, runners at the start can line up where it's appropriate for their pace, instead of trying to push their way to the front. For longer distances, the chip also records splits at various points along the course, such as the half-marathon mark during a marathon. This feature is helpful for your friends and family members who may want to track you online during your race.
Of course, one drawback of timing chip technology (although most runners would never admit it) is that runners can no longer "fudge" their race times by subtracting more time than it actually took for them to cross the starting line. The chip doesn't lie.
Also see: Running Acronyms and Their Meanings