Independent comics refer to alternative comic books that were not acceptable to the mainstream publishers. They tended to have off-color topics that were not embraced by a wide section of readers. They make up a very small percentage of the comic book market. This is not always the case because it is possible to find really good comics in this category with exceptional artwork and storylines. It is just that the main comic book publishers rejected them.
Small presses that do not print a large number of copies of the comic book at one time usually publish independent comics. There are probably only several issues a year rather than a monthly issue. Some of the popular titles that you may be familiar with include:
Students operating under the University's publishing regulations publish some of the independent comics. This gives them a forum for their creations and the comics may actually be part of their course requirements. There are conventions held where independent comic book creators can showcase their work. Some of these specialize in mini-comics or have graphic comics of different genres.
Some comic creators and artists self publish their work as independent comics. With the advances in desktop publishing, this is very easy to do. Comic book artists and writes can set up their own mini-publishing company in their own home and take care of all their own marketing and sales. It takes time to build up a following but with a good story line and good artwork, this is one way to make a profitable living in the comic book industry. Once you have published your own work and it is selling, then the comic book publishers will probably express an interest in seeing what you have done.