Trainers recommend interval workouts for a couple of reasons that I don't really understand.* But in short, they're great for your heart, since you get your heart rate really high during the intense times. And the intervals also force you to push yourself without exhausting yourself - maxing out your calorie and fat burning potential.
From a biological standpoint, the early human hunter-gatherer lifestyle likely lent itself well to interval workouts. The day long pursuit of prey, with the sprint lunge attempt at the kill. These were the very first interval workouts.
Our body was designed assuming interval workouts. But in our 21st century lifestyles, they don't happen organically throughout the day. So, we have to pretend we're boar hunting. Only the treadmill has replaced the hunt.
* Please help with the science-y stuff in the comments.