What is the context?
This request comes after Jesus has healed people and answered the accusation that His power comes from Satan. Some scribes and Pharisees now ask for a sign. The demand belongs to that setting of resistance to works they have already seen.
The word for demanding a sign is ἐπιζητέω, epizēteō (eh-pee-zay-TEH-oh), to seek after or demand. Thayer's entry explicitly includes this saying. Jesus does not accept the demand as the condition on which His hearers may keep postponing a response.
He names the sign of Jonah. The explanation continues immediately in verses 40–42: His own coming death and resurrection are compared with Jonah's time in the fish, and the response of outsiders is placed beside His hearers' resistance. These two verses introduce that larger answer.
How is this passage commonly understood?
Christians commonly read this as a rebuke to resistant hearers demanding further proof, rather than a rejection of every sincere question about God. Wesley on Matthew 12:38–40 emphasizes the signs already received and understands Jonah as pointing toward Christ. The US Catholic bishops' notes on 12:38–42 likewise connect the demand with refusal to accept Jesus' works and explain the Jonah sign through His death and resurrection.
Where does this fit in God's plan?
Jesus' answer points forward to the center of His saving work. In the following verses He connects Jonah's experience with His own coming passage through death. Matthew 16:21 later speaks plainly of His suffering, death, and resurrection on the third day.
The sign will be more than another display requested by opponents. It points to the Savior giving His life and being raised, the events Paul places at the heart of the gospel in 1 Corinthians 15:1–8.
What is our position?
Should We Seek Signs From God? reads this as a warning against demanding another sign while resisting what God has already revealed. These leaders have already seen Jesus' works; the study distinguishes their demand from sincerely seeking to understand and obey Him.