(there are many different types of concept artists)
With any production (film) there will be many types of concept designs all just as important as the other. The first one that'll most likely come to mind is the Character Designer, the job of this this group or person (depending on the size of the department) is to visualise how characters will look such as what clothes they'll wear, how their hair is cut and even how they'll move. If the character is un-human it's also the designers job to design how the look physically. Next there will be Creature Designers (if there is a call for a range of creatures in the feature) their job is the same as the Character Designers, only they focus on the creatures of the feature, then there is Background Designers who create the worlds for these creatures and characters to live in. After this we have veichle and prop designers who, you guessed it! Design the machines and items of the worlds they're creating. Now whilst they're seperated into groups they still work together to make sure their designs fit together well. All the designs will be professionally trained illustrators each with specialities in certain fields, for example Character Designers may have an understanding or experience in fashion where as Background Designers will likely have experience with archetecture and Prop Designers will have worked in product design. There will then be points where the script writer or produce will visit the department and give advice on what he likes and dislikes from there the team will go back and work on their ideas until the writer/produce is completely happy with the body of work. The concept art is then passed onto next group of people who'll bring the film closer to realisation.
I got most of this information from watching the special features on the bonus disc of Starwars: Episode III: Revenge of The Sith. I found that it was really helpful to learn that there were many different types of concept artists that all come from different backgrounds, but the the one thing they had in common was that they were all very skilled and thats possibley the most impressive thing about these people, it that they have the skill to illustrate their amazing imaginations.