This was not the first time the Jews became enraged and attempted to stone Jesus (cf. 8:59). Their anger was kindled by Jesus affirming His unity with the Father, which they considered blasphemous (cf. 10:33; Lev. 24:16). Although the Jews technically didn't have the power to exercise capital punishment at this time since they were under Roman rule (cf. John 18:31), that fact didn't always stop them from trying (and sometimes succeeding - e.g., Acts 7:58).
"Many good works I have shown you from My Father. For which of these works do you stone Me?" - Jesus knew that He was living a sinless life, and He here tries to make the Jews aware of that life by asking them to point out what work He had done that had so offended them. He is essentially asking them to test His claim of oneness with the Father by considering His miraculous activities.
Jesus correctly referred to His miracles as "good" because in every instance they brought blessings to those who were suffering and sorrowful. Additionally, these works were only made possible through the Father's power (cf. John 10:21). If these Jews had understood this then they would not have been charging Jesus with blasphemy on this occasion.
But, the Jews insisted upon judging Him by His words without taking His works into account at all. So, while Jesus maintains that His actions prove His claim, they automatically discount His claim as blasphemous for it came from the lips of One who, in their minds, was only a man. Their minds were made up and their hearts were hardened. They were not even willing to consider that His statement could be true in spite of all the miracles they had witnessed. Sadly, though they never denied the reality of Jesus' miracles, they did deny that the power for such came from God. They chose rather to attribute the miracles to demonic powers (cf. Matt. 12:24). Thus, in this context, they believed that Jesus was worthy of death for His words. Interestingly, it is worthy to point out that Jesus' statement struck his opponents in such a way that they felt obligated to pause and reply to Him and attempt to justify their actions.
We will continue studying this narrative in our next lesson.