A running shoe drop, or heel-to-toe offset, is the difference, measured in millimeters (mm) between the height of the shoe sole in the heel area vs the height of the sole in the toe area.
For reference, traditional running shoes usually have an offset (drop) of 12mm. Low drop are considered shoes with a drop between zero (called zero drop) and 4mm. Everything in between is also possible.
The logic is: shoes with a higher heel will favor heel strike during running, while shoes with a zero or low drop will favor a more forefoot or midfoot running gait. It is largely a matter of preference, but running on your toes requires a completely different set of muscle activation and switching from one kind of shoe to the other without proper conditioning and a very gradual approach might result in injury.