It's very important, especially in freelance illustration, to have a unique and recognizable style. Sometimes, however, advice on developing a personal style can be confusing or contradictory. After reading many, many blog posts about style and listened to many speakers talk about style, here's the core of what I think most people are trying to say:
Consistency in style, versatility in content.
Your style must be consistent, especially when you are just starting out. Art directors want to be able to know exactly what they're going to get from you. If you don't have a long track record of professional work, your portfolio needs to be as solid as a rock. It needs to say, "I'm a master at what I do." If your portfolio has a few pieces that are kind of graphic, a few that are realistic, a few that are cartoony, no art director will hire you. Art directors don't want someone who can do a little of everything, they want someone who can do one thing really, really well.
Artists often say, "But I don't want to pin myself down! I enjoy lots of different styles and mediums!" In that case, choose your most marketable style and most proficient medium and develop a portfolio with it. You don't have the give up on your other styles forever, just enjoy them in your free time while pushing one particular style as your brand. If an art director does seem interested in something a little different, you can possibly bring those other styles out.
That doesn't mean you should draw one thing over and over again. You should show a good range of content in your illustrations. As Lauren Panepinto said, art directors don't have much imagination: they will hire you to draw the kinds of things you put in your portfolio. "If you don't have horses in your portfolio, I'm not hiring you to do a horse," she said. If your portfolio only contains dragons, dragons, dragons, that's the only thing you will be hired to draw. Good luck making a living off of dragon commissions.
So if you do character designs, don't just draw young attractive people. Draw old people, fat people, children, various ethnicities. If you do children's books, draw contemporary children, historical children, fantasy children, and children of various ethnicities and body types and expressions. Draw all kinds of animals. But all of these things should have a consistent style.
Consistency in style, versatility in content is the goal.