CV is short for Curriculum Vitae, which is a longer and more detailed version of your resume. If an employer asks you for a CV, this means he wants information about research you've conducted, places you've been published and awards you've been given, for example. CVs are usually asked for in the education and health industries, but are also used in countries other than the United States.
Start off with your same heading information: name, address, phone number and email. If you're applying for a job not in the U.S., you'll want to include other personal information such as gender, date of birth and place of birth (when in doubt, ask the employer what personal info you should add). This is normal for jobs in Europe and other countries, but not the United States.
Copy your educational information and work history from your resume. These should be the same on your CV, but leave out any work experience that's irrelevant to the position you're applying for. Your CV may have a generally different format than your resume, since the CV is so much longer, so adjust accordingly.
Include all honors, awards and other recognitions you've received. This is important on your CV because the employer wants to know that you've done well in your field. If you don't have any awards, include things like graduating with honors from college, or being in an honor society.
Write down all research you've conducted or places your work has been published. For a research position, this will be vital. Your potential employer wants to know that you've actually done some research and are capable of performing the job. You can also add relevant skills to the position you're applying for.
Include all presentations you've made, grants you've received, licenses you have and any groups or associations you're a part of. Any other pertinent information can be added at the bottom too, like volunteering experience or relevant traveling. At the end, include a blurb about references being available if asked for.
If you're having trouble formatting your CV, look to samples online for help.
Since there's so much information needed on a CV, it's even more tempting to exaggerate yourself. Don't do it. if your employer finds out, you surely won't be getting that coveted position.