Left-foot braking means applying the brake with the left foot while your right foot is on the gas and the car is moving forward. It’s one of the most important skills I’ve learned. It makes progress over rocks and obstacles much smoother by reducing suspension movement as tires come off of obstacles. Chassis impacts with said rocks and obstacles are thereby also reduced.
Imagine a tire going over a rock. Even pressure on the throttle makes for a smooth climb to the top of the rock. Even pressure on the brake makes for a smooth descent down the other side. Gas and brake at the same time covers all of your bases, as some tires may be climbing while others descend.
There’s a second benefit. In a vehicle with open front and rear differentials (most 4x4s) getting into a crossed-axle situation (in which one wheel on each axle has lost traction) will halt forward movement. Squeezing the brake while keeping your foot on the gas can reduce wheel spin in the lost-traction wheels and transfer torque to the wheels with grip. In my experience though, this doesn’t work if the truck is up against big obstacles. That said, if you happen to get cross axled on a rutted but flat road, it’s a good trick to have up your sleeve.
This video does a good job of explaining both scenarios. If you haven’t already, practice left-foot braking the next time you’re out on the trail. Your smoothness over obstacles will be like night and day. Once I learned, I wondered how I ever got by without it.