Thick metal tends to hold on to heat.
Thin metal radiates that heat.
You have two pans of identical shape and size, on two identical burners in front of you. The only difference being that the pan on your left is thick seasoned 1/8 inch plate steel, and the pan on your right is a modern coated teflon pan made of steel that is just above paper thin, or has multi layers in an attempt to make it perform better.
The two pans have similar surface area, but totally different mass. The thin pan on the right radiates as much heat as is put into it, meaning you've got to keep the heat up in order to get semi even cooking temperatures. Sure, it heats up fast, but it cools off nearly just as fast! Plus, there are hot spots right above the burners, and that coating has already started flaking off into your food.
The thick pan on your left has much larger mass in relation to it's surface area, meaning that it cannot radiate and lose as much heat as its thinner neighbor. All that mass means it takes a bit longer to heat up and get to temperature, but it means it holds that heat better, and more evenly. The hot spots at the burner are diminished in favor of even distribution of that heat, as the colder parts of the pan begin to soak up that energy. Soon, that pan is super uniformly heated, and ready for cooking!
Since the greater mass means more even temperatures and lesser heat loss, a thicker pan requires much less heat than its thinner counterparts, meaning lower burner temperatures, and a longer warm up prior to cooking, but better results!
The biggest piece of advice I can give to newcomers to both carbon steel and cast iron is:
"Turn down that burner!"
Often, people use seasoned pans like a thin coated pan needs to be used: Higher heats, as your cook surface is losing heat nearly as fast as you're pumping it in. Seasoned pans don't need that much heat during normal use. You'll find that for most general cooking, setting your burner to a medium low (or sometimes lower) setting is perfect, and helps to preserve the seasoning of your pan, especially during the sensitive break in period.
Turn that burner down, and let that pan get up to temperature before you start cookin'. Your pan will thank you, develop that wonderful seasoning faster, and be easier to clean and maintain!
Happy cookin', friends!
And thanks for reading!