The Complete Jewish Bible tells the story this way:
As he went, with the crowds on every side virtually choking him, a woman who had had a hemorrhage for twelve years, and could not be healed by anyone, came up behind him and touched the tzitzit on his robe; instantly her hemorrhaging stopped. Yeshua asked, "Who touched me?" When they all denied doing it, Kefa said, "Rabbi! The crowds are hemming you in and jostling you!" But Yeshua said, "Someone did touch me, because I felt power go out of me." Seeing she could not escape notice, the woman, quaking with fear, threw herself down before him and confessed in front of everyone why she had touched him and how she had been instantly healed. He said to her, "My daughter, your trust has saved you; go in peace." (Luke 8:42-48)
What are tzitzit, or tzitziyot as they're sometimes called? They are the tassles or fringes worn on special garments, in accordance with Numbers 15:37-41:
ADONAI said to Moshe, "Speak to the people of Isra'el, instructing them to make, through all their generations, tzitziyot on the corners of their garments, and to put with the tzitzit on each corner a blue thread. It is to be a tzitzit for you to look at and thereby remember all of ADONAI's mitzvot and obey them, so that you won't go around wherever your own heart and eyes lead you to prostitute yourselves; but it will help you remember and obey all my mitzvot and be holy for your G-d. I am ADONAI your G-d, who brought you out of the land of Egypt in order to be your G-d. I am ADONAI your G-d."
Even today, all over Jerusalem and Israel, Jewish men wear tzitziyot -- like this guy waiting for the train. It's a physical reminder to "be holy for your G-d", for the wearer and those around him. It definitely makes the wearer set apart, as G-d has called us to be, according to His Word.