Did you know that the word freelance comes from a knight or mercenary who would sell his services to any lord willing to pay- hence he was a "free lance?"
In this same way, a freelance writer is a writer who works for a company or individual on a contractual , or project basis. These "contractual" positions don't even necessarily need to have a formal contract in place (although that's probably in your best interest as a writer) , but what they do have in common is that they are a project or piece of writing with a set time frame and a clear goal. After the project is complete, the free lance moves on to the next project.
There are many different kinds of freelance writing, such as business writing, marketing writing or web writing. On the other hand, some freelancers focus solely on querying and writing for magazines, anthologies or newspapers, while still others serve non-profits through grantwriting and proposal development.
Once you dive into the world of freelance writing, you'll begin to have a good grip on your strengths and weaknesses, and be able to target the jobs that best showcase your abilities. Once you figure out what you're good at, and begin to parlay that talent into project after project, you will then truly be a "free lance."