A lot of people ask me "How can I run faster?", and my usual reply is "Interval training"! Short fast runs (speedwork), including interval training and hill training, will help your legs get used to running faster in the long term, whereas long slow runs will build up your endurance so you can run further.
There is a scientific reason though, and it's about types of muscle.
I blogged a few years ago about why we need to vary the types of run we do, and the post is pasted below. It also explains why we should bother to train to heart rate (see also my blog on heart rate zones).
Our body contains two types of energy source: glycogen and fat. When you begin a run or workout, your body "fires up" and starts to burn glycogen without oxygen (anaerobic metabolism). This warm-up phase lasts a maximum of 2 minutes, after which your body begins to burn the glycogen with oxygen (aerobic metabolism). After 30 minutes of your run or workout you begin to burn fat aerobically; this process is the most efficient way to produce energy and is what will get you through an endurance race. You still need glycogen as a back-up (for dealing with hills and a sprint finish!), so training your body to burn fat rather than glycogen (and therefore saving this vital energy source for "emergencies") is important.
Muscles are formed of two types of cells (or fibres): slow-twitch and fast-twitch. Slow-twitch cells have a high oxygen content (for aerobic metabolism) and burn fat; they are therefore most important for endurance. Fast-twitch cells create energy from glycogen without oxygen (anaerobic metabolism); a by-product of this process is lactic acid, which creates that painful burning sensation when you train hard. Increasing the amount of fast-twitch muscle cells will help you deal with this burning pain (sprinters have a lot of this muscle-cell type).
How the science fits with training
"Easy" training days at 70% recovery heart rate increase the number of slow-twitch cells, thereby teaching your muscles to burn fat (and saving your glycogen for another day). By increasing your muscles' fat-burning potential you are not only getting fitter but also boosting aerobic capacity, the ability to burn energy with oxygen.
But you do need some capacity for anaerobic metabolism (without oxygen, glycogen-burning); anaerobic metabolism is going to get you started on a run or workout and will propel you up a hill quickly, but will make your muscles burn from the pain of lactic acid build-up. A "hard" training day or interval training---when you run for short distances at your 85% threshold ceiling heart rate---helps your body develop more fast-twitch cells to deal with the pain of lactic acid build up.
"Hitting the wall" (basically, when your legs stop working) happens when you've run out of glycogen. So easy training days---teaching your muscles to burn fat---are really important so you have glycogen available when you need it.
That's my very simple explanation of why it's important to run or workout at these two different heart rate zones. For more details I suggest you read Heart Monitor Training for the Compleat Idiot by John Parker or borrow a book from your library on sports biochemistry or muscle metabolism (there are lots out there).