To freelance is to work independently, instead of for a long-term employer. If you do freelance work, you’re free to say yes or no to any project. Anyone can work freelance (as a freelancer), but it’s often a writer or artist.
To freelance is the opposite of working for one employer full-time and long-term. A freelancer — who could be a writer, a designer, or one of many other jobs — probably has many employers. The word comes from the Middle Ages, for "medieval mercenary warrior," which makes sense, since a mercenary is someone who fights for hire. It’s a free (not bound by a country) lance (sword). The pen is mightier than the sword, so these days freelance often refers to writers.