The amount of heel-toe drop of a running shoe is defined as the amount higher off the ground your heel is than your forefoot when standing in the shoe. This is due to the difference in thickness of the sole under these locations of your foot. For example, a shoe with a “10 millimeter heel-toe drop” (that of a “traditional” type running shoe from the 1980′s to present) raises your heel 10 millimeters (about 3/8 of an inch) higher than your forefoot when standing. “Zero” heel-toe drop would be the equivalent of standing barefoot; although with shoes on, there would be an equal thickness slab of shoe sole under both the heel and the forefoot.
Although two different shoe models can have the same amount of heel drop as each other, they can differ in overall thickness of the sole, a parameter known as the "stack height". In the example provided, the stack height under the heel is 24mm, the stack height under the forefoot is 20mm, and the heel-toe drop is 4mm (24mm-20mm).
The concept of incorporating “less heel-toe drop” into running shoes came with the popularization of the “minimalist” running movement over the past 10 - 15 years. The argument for zero heel-toe drop being optimal is based on the assumption that the barefoot state, also zero heel-toe drop, is the foot's "natural", and therefore best alignment. The flaw in this argument is that it does not account for the alterations in human structure, function, and biomechanics as a result of wearing footwear with 10 mm or more heel drop for most activities people perform on their feet throughout their lives.
Studies have shown that running biomechanics are altered by alterations in the amount of heel drop the shoes have. Two general findings with respect to less heel drop were less heel strike/more midfoot to forefoot strike when the foot contacts the ground, and increased calf muscle work. There are potential benefits to this alteration in running mechanics for some runners and disadvantages for others.
In clinical practice, I observed that people who tried to switch to significantly less heel drop without significantly reducing the amount of mileage they ran in the new shoes quickly developed injuries during the process, whereas those who gradually changed the amount of heel drop of the shoe and/or the amount of mileage introduction in the new shoes had far less problems. The benefits of changing heel drop, however, are that certain long-standing injury patterns for some people can improve or resolve with successful transition to a different heel drop, be it lower or higher.
The take home message here is, if you wish to alter the amount of heel drop in the shoes you run in, for whatever reason, do so gradually. For example, if you are in 10 mm drop shoes, first go to 6-8 mm drop shoes for at least a month or two and see how you respond before proceeding further. Working with an experienced running footwear expert at a reputable running shoe specialty store can be helpful in determining what is right for you.