A concept artists job role is presenting and generating the visual style of the game or film under the direction of the art or creative director. Being a concept artist holds a lot of responsibility in createing the starting blocks for the visual style and overall feel for the game which gives them a lot creative freedom. However, a large part built into the role of being a concpet artist is being able to take constructive criticism and using it to push the ideas that are on paper and you may really like and developing them further for the needs of the project.
Weta workshop who created the props and concepts for the great sci-fi film District 9 are a great example of a good art direction team and group of concept artists. A main feature in the film is

Concepting is really the fleshing out of ideas not creating a piece of art that gets a thousand hearts and wow your awesome on deviant art. It's often seen as just making cool digital paints or illustrations that show an interesting idea and not something that you could really get a physical end product from. It seems a lot of people aspire to be a concept artist without knowing what the job really entitles.
I feel that i am a victim of not working through ideas in the aim of making something that people go wow at sometimes, though the vehicle project i have been working on recently has really shown me the fun and need for working through ideas and developing them further to make sure that the same old clichéd ideas don't get footprinted in the designs and allows the rubbish to be put on paper and removed from your brain and clear the way for something original.