Jesus is teaching in a synagogue on a sabbath, as he often does (recall 4:15-16, 31-33; 6:6).
This time, he meets a woman who's possessed by a spirit that has caused her to be hunched over for eighteen years.
As soon as he sees her, Jesus deems her "free" (13:12 NRSV) or "loosed" (KJV) from her condition. He's still doing what he said he would in 4:18-19.
He lays his hands on her and she straightens up, giving God requisite props.
But—surprise, surprise—the chief of the synagogue is annoyed that Jesus did this work on the sabbath.
The chief argues that six days are for labor, and he has Exodus 20:8-11 and Deuteronomy 5:12-15 to back him up. Why can't Jesus heal her tomorrow?
If this whole fiasco sounds familiar, it's because Luke loves to weave themes like this in and out of the story.
In response, Jesus calls the chief and anyone who agrees "hypocrites" (13:15). After all, they themselves do exactly what they're condemning.
Everyone takes care to untie their farm animals on the sabbath in order to give them food and water. The possessed woman is a fellow Jew, and Satan's held her tied up for eighteen years.
It's inconsistent, even inhuman, to argue that it's a breach of the sabbath to untie her from her demonic affliction, while it is not a breach to untie a silly cow or donkey. (Check out Jesus's similar logic in 6:9.)
This pretty much puts all of his opponents to shame, and the crowd is psyched. Go Jesus.