What is a concept?

A concept is defined as a general idea or notion.
I consider a concept to be a rough idea.
Something I usually conceive at 1 a.m. by scribbling out indecipherable notes to the light above the kitchen sink.
A sketch started on a coffee stained napkin or on the back of a receipt.

These posters are considered concepts, but they look far to refined to be a "concept".
They were considered to be the promotional posters for the London Olympics 2012.
  



The Official posters were done by a collection of British artists.

 

The individual approach to what the games meant to England seems to be expressed, but without the harmony of a single focus. If one style or approach had been decided on and then reworked, it would have been a more comprehensive look.

The focus of the posters would have been on the Olympic Games, not the artists.

While I love that they were done in a national spirit by using these artists, I don't feel these official posters were as refined as the concepts. Which brings me to question the very definition of a "concept" poster. 
Now, I know the London Olympics have come and gone, but I just stumbled upon these images.  

What do you think? 
What is the definition of a concept?