When it comes to writing, style is perhaps one of the strongest things a reader will remember. To the point, style is basically two things - - genre and tone. As human beings, we all like to classify and categorize things, and genre is one of those tendencies made manifest when it comes to media (literature, movies, animation, television, etc.). A genre is basically a set of conventions used to help classify a certain type of media. For example, in a Western film, a viewer expects cowboys, Indians, gun fights, and horses -- these are just some of the elements that make a Western a Western. In many ways, a writer makes use of these conventions to help detail the setting and theme of the story she or he is trying to write. Genre, can, in some ways, be a universal kind of thing, and in some ways very impersonal to the writer.
Tone, on the other hand, is very personal. Tone is the "attitude" a writer has toward their own story. A reader can "hear" the tone of a writer when reading about certain types of characters or situations. For example, when reading Fritz Leiber's work, a reader can ascertain through dialogue and the narrator that Leiber has a very sarcastic, tongue-in-cheek, and dry sense of humor. It lends him a very distinct tone, and because of that and the genre he works in, a distinct style.
In closing, style identifies a writer more so than what he or she writes. It can be both a blessing and a curse akin to that of great famous actors who get known for certain characters they played or pigeon-holed into certain roles (Tim Curry almost always plays a villainous character). But when all is said in done, all the great writers have their own distinct style; it just takes experience and time to have your style not be a lead weight.