It means a really, really big mistake. Really big. One that will affect many people and/or things, and the effects of which will be felt for a long time.
The original definition of "epic" is a long poem, usually about the achievements of a hero, narrated in a grand style (e.g. the Iliad). These days the word means anything long, drawn-out and grand; movies are often said to be "epics." It's even become slang.
[not a teacher]