To be in a delicate situation; to be on the edge of danger or ruin.
An 'eggshell' is the thin, white outer coating of an egg.
The shell is very thin and breaks easily. So if you are 'walking on eggshells' you are in a situation where you could break something (or get in trouble or ruin
everything) very easily.
Synonym:
walking on thin ice
1)
Ever since I smashed their car,
I've been walking on eggshells with my parents.
2) We're walking on eggshells with our landlord -- she told us that if we have
one more loud party, she's going to kick us out of our apartment.