"Now He was teaching in one of the synagogues on the Sabbath. And behold, there was a woman who had a spirit of infirmity eighteen years, and was bent over and could in no way raise herself up. But when Jesus saw her, He called her to Him and said to her, 'Woman, you are loosed from your infirmity.' And He laid His hands on her, and immediately she was made straight, and glorified God. But the ruler of the synagogue answered with indignation, because Jesus had healed on the Sabbath; and he said to the crowd, 'There are six days on which men ought to work; therefore come and be healed on them, and not on the Sabbath day.' The Lord answered him and said, 'Hypocrite! Does not each one of you on the Sabbath loose his ox or donkey from the stall, and lead it away to water it? So ought not this woman, being a daughter of Abraham, whom Satan has bound--think of it--for eighteen years, be loosed from this bond on the Sabbath?' And when He said these things, all His adversaries were put to shame; and all the multitude rejoiced for all the glorious things that were done by Him."
It was Jesus' tradition to teach in the synagogues on the Sabbath days when possible. Such was an ideal time to teach those Jews who were gathered.
Although the text does not explain such explicitly, it seems that this woman's infirmities were the result of being possessed by a demon. There are two points of evidence for this conclusion: (1) the woman was described as having a "spirit of infirmity" and (2) Satan had bound her (cf. 13:16). One can only imagine the suffering this woman would have endured for nearly two decades!
"Woman, you are loosed from your infirmity" (Luke 13:12). Jesus' compassion is clearly seen in that He isn't even asked to heal this woman, but He willingly does so (e.g., 7:11ff). In addition to His verbal statement, He "laid His hands on her, and immediately she was made straight." She is overjoyed at this miraculous healing and glorified God!
However, the synagogue ruler doesn't glorify God for this miracle. Instead he angrily speaks to the crowd - "There are six days on which men ought to work; therefore come and be healed on them, and not on the Sabbath day." There are several things wrong with his statement: (1) There is no evidence that the woman came with any intention of being healed, (2) he was angry at Jesus and should have directed his words toward Him and not the crowd, and (3) what Jesus did is not correctly classified as "work" that would have been divinely prohibited on the Sabbath (though it most certainly did violate their man-made traditions).
Although the ruler may have been too afraid of Jesus to rebuke Him directly, Jesus is not afraid to boldly declare the truth to this man. He labels the synagogue ruler a "hypocrite" and then explains why this man (as well as Jesus' other "adversaries") were two-faced. First, they were hypocritical in that they disguised their hatred for Jesus under a pretended zeal for the Sabbath. Second, they were hypocritical in that they were inconsistent in their behavior. They applied their Sabbath rules strictly when considering the actions of others, but when their own interests were involved they indulged themselves.
Jesus offered a specific example of this - "Does not each one of you on the Sabbath loose his ox or donkey from the stall, and lead it away to water it?" (Luke 13:15). Certainly many of those present had that very morning led an animal to water and did not think that they were in error in so doing, yet they fumed at Jesus for healing this woman on the Sabbath. Jesus' point logically is this: If you can lead an animal to water without breaking the Sabbath, then certainly I can heal this woman! Why should they criticize Jesus for doing such a merciful act to this suffering woman, when they had done a merciful act to a less important life form? This woman had been afflicted for 18 years! Her needs were far greater than the daily needs of an animal for water. They could not rightly criticize Him without criticizing their own activities.
Jesus also mentioned that this woman was a "daughter of Abraham" to further stress the value in healing her, even on a Sabbath day!
Jesus' reasoning was devastating to them and they were put to shame. They had no response and the crowd rejoiced over the miraculous works and wise words of Jesus.