Who was the lady who touched Jesus's clothes?

I believe your question is in reference to a woman mentioned in the Gospels of Matthew, Mark, and Luke. These portions of the Gospels describe many miracles performed by Jesus Christ, including healing the sick and impaired. As the story goes, a woman had been suffering from blood loss for twelve years. She had seen many doctors and spent all her money on treatment, but her condition only worsened. When she saw Jesus passing through the town, she reached forward, touched his clothing, and was instantly healed. Jesus is said to have then turned to her and said, "By your faith, you are healed." 

The term most commonly used when referring to this woman's ailment is "discharge," which is used throughout the Bible to denote an emission of bodily fluids considered to be the result of something unnatural (like an illness) and which causes spiritual impurity. It is also quite specifically used to refer to emission of fluids of the urogenital system. This story took place in Gerasenes, which was in the region of Galilee and where the people were Jewish. Presumably, this woman had been socially ostracized for her persistent bleeding. She would not have been allowed into public houses of worship and may have even been somewhat isolated from her family. 

It is important to note the woman merely touches Jesus' garment, not him physically, and still she is healed. This bears reference to a few traditions in Jewish culture—appropriate physical contact and transmission of power or holiness through cloth. In both the Talmud and the Old Testament, it is prohibited for unrelated or unmarried people of different sexes to touch. For this woman to reach out and touch Jesus physically, or for him to touch her, would violate a social rule about appropriate physical contact. What's more, this woman was considered spiritually impure, an outcast, and even her husband may have had limits on physical contact. (Assuming she was married before the onset of bleeding.) Jesus, a Rabbi, acknowledging the woman is very powerful indeed, for he performed a spiritual and bodily miracle on her even though she was considered impure. Finally, transmission of power through cloth is something which has a long tradition in Judaism. The Torah is wrapped in special cloth, called the clothes or dress, and when it is paraded for blessing, people may reach out to touch the cloth or touch their own garments to the Torah to receive some of its special power. It is like transferring a blessing from some holy entity (Jesus, in this example) without profaning or desecrating the holy thing by contact.

In addition to the physical difficulty of bleeding for twelve years, this woman was likely to have struggled emotionally and socially, too. Her ability to interact in normal daily life would have been greatly impaired by her constant loss of blood regardless of any spiritual qualities associated with her condition. I would also like to mention that this woman may represent one of the earliest descriptions of a woman with a bleeding disorder, such as von Willebrand Disease. 

As for who this woman was, we do not know anything about her beyond that she was from Gerasenes and had suffered blood loss for twelve years.