At sundown, they brought to him all who were sick or possessed with demons. And the whole city was gathered around the door. And Jesus cured many who were sick with various diseases, and cast out many demons... (Mark 1:32-34)
In his public ministry, Jesus seems to be known first not as Messiah, not as Savior, not as Son of God, but as a healer. This - probably more than his teaching - is what seems to have attracted crowds. And why not? Today health care is one of the things we will pay the most for. When you are ill or suffering, finding relief and especially a cure becomes supremely important.