This is a term not created by the Trio themselves.
This is a word that does not originate from The Trio, but from the interwebz. The term is commonly used along internet goers and in various situations. Motivational posters are often used to display fails. They also show off in LOLcat pictures and the like. A fail describes an action that is not a win. Simple enough, yes?
The term Fail is also used by many others in real life who are not the Trio. Although those people aren't nearly as awesome. Anyone is free to use this term as it does not belong to the Trio.
The trio uses it when something stupid happens or to describe something stupid. It can be used in various negative contexts. However it is motly humorous when used by the Trio.
An example of Random Babbling with the term Fail being used in it follows as:
Sushi: I made a banana phone! *holds up orange*
Kerfy: FAIL. This is a banana phone! *holds up apple*
Sushi: I made a tower yesterday and spent 200 hours on it and it got knocked over by a stationary pebble.
Kerfy: Awww...that fails, man.
Sushi: Yeah I know...OTL
Sushi: SO I HERD U LIEK-
LI3: -To tell you tha you fail :3
Sushi: ..... oAo
Sushi: YES. I ARE WINNER.
The word fail is used in several places along the Trio's time. A majority of the time would be in everyday speech and notebook spaces. When not used by the Trio, the motivational posters and caption pics on the Interwebs show many types of fails, both mild to insanely severe (and funny).