I am not going to rewrite what Wikipedia says so…
Heel-and-toe shifting is a driving technique used mostly in performance driving, although some drivers use it on the road in everyday conditions in the interest of effectiveness. It involves operating the throttle and brake pedals simultaneously with the right foot, while facilitating normal activation of the clutch with the left foot. It is used when braking and downshifting simultaneously (prior to entering a turn), and allows the driver to “blip” the throttle to raise the engine speed and smoothly engage the lower gear.
There is a lot of benefits coming from this technique, the main one probably is to avoid the fall of the revs on the corner exit after downshifting. This usually feels like a lack of engine power and gives you a non optimal acceleration.
Racing theory says that exiting a corner with an adequate speed is key to being faster, mastering these foot techniques should be a mandatory goal for every racing driver.
The best possible explanation about every step of this technique is drivingfast.net. Diagrams are very clear and precise.
And if you want to see a nice footwork combining heel and toe and left foot braking, take a look to this video.[youtube https://www.youtube.com/watch?v=TnhFAy-hbow]
Practice makes perfect.