A stack of zombies refers to several zombies in the same location.
If 6 zombies were to occupy the same location, the map would show them as "6 zombies." Zombies are usually quite anonymous: their profiles are only revealed when they perform an action, or have their DNA extracted. In that vein, if a human were to walk onto the hypothetical 6 zombie square, he would not be able to attack individual zombies. Instead, he could only choose "a zombie" from the target menu, which would target the zombie who had been inactive the longest, which could be thought of as being at the top of stack. The only time when a human can actually recognize a zombie among a group of zombies, without performing an action, is when the zombie is in the human's contacts list.
A stack of zombies is called a mob or a horde when it is sufficiently large.
Zombies with brain rot can take advantage of the stack and the way that DNA Extractors operate to clog revive points. There is currently no way to move a zombie up/down the stack with a DNA Extractor; the least active zombie will remain on top unless they move or are killed or revived. Some players consider this to be griefing, though many others find it a viable zombie tactic.
"The stack" can also refer to the list of survivors in room descriptions and drop down menus. When a survivor is active, they go to the bottom of the list. This means the list is sorted according to how recently survivors were active, with the most recently active at the bottom.