When you take a dump and flush it, but some or all of your turds come back up (back from the dead, hence the term "zombie shit").
Example: Dude, if you happen to take a zombie shit again, could you please flush a second time?
A shit you're sure you flushed but somehow is still in the toilet later.
Mom: WHY DIDN'T YOU FLUSH?
Son: I did!
Mom: Go look!
Son: FUCKING ZOMBIE SHIT