This is due to what researchers call the Barnum principle. Here I am using Snyder's (1977) definition: "The Barnum Principle refers to the method of listing many general traits so that almost everyone who reads the horoscope thinks that these traits apply specifically to him or her. But, in fact, these traits are so general that they apply to almost everyone."
However, studies indicate that horoscopes have no validity. Validity means that something measures what it claims or is supposed to measure. "Researchers found that the 12 zodiac signs were no better than chance at identifying traits for a particular individual." (Svensen & White, 1994)
I also understand that many people read them and find them enjoyable without the belief that they are infallible or accurate predictors. They are entertainment. If a horoscope says, "This is your lucky day," a person who had no cavities at his dental checkup and one who won $6 million dollars in the lottery, can both claim that their horoscope was right on.