You get up the stairs faster. Seriously, though, I've also recommended that some athletes take stairs two at a time, particularly for developing strength and stability through the hips. Think about what happens when you reach your foot up and out to reach for that second step. Your knee rises high enough that your thigh is about perpendicular to your body, like it would be at the bottom of a lunge or one-legged squat. Then you have to balance and support yourself on that leg and then lift your entire weight with it. While that takes a lot of leg strength, it also stimulates muscles throughout the hips in order to keep your pelvis level as you step up.
Taking steps two at a time is a great exercise for people who enjoy hiking in mountainous regions and athletes who participate in non-weight bearing sports, like cycling or swimming. Hip stability and strength is key for reducing lower back pain as well, so it's a good exercise for people who struggle with back pain, as long as they can handle the exercise without causing more pain.
To add to the challenge, you can take stairs two at a time and add a speed component to develop power in addition to strength. Power is the ability to deliver force quickly, so bounding up stairs two at a time is a great progression from merely walking up stairs with bigger steps. Either exercise is a good way to get a quick workout when you're stuck inside, either because the weather is terrible outside or you simply can't get out to complete another workout. I frequently use stair bounding workouts for athletes who work in high-rise office buildings because they can make great use of the continuous stairwells.