Why did Christ perform wonders and signs during His earthly ministry?

Christ performed wonders and signs during His earthly ministry to prove to the Jewish nation that His works were God's doing. Just as Moses showed signs in Egypt, these miracles authenticated that Jesus was the Christ, Israel's promised deliverer, and that God was working through Him.

Les explains that Stephen, in Acts 7, draws a parallel between Moses and Christ. Moses brought Israel out of Egypt after showing wonders and signs in the land of Egypt, and he continued to show signs at the Red Sea and in the wilderness forty years. Les teaches that Christ's earthly ministry was almost the same: He had to show wonders and signs to prove to the Jewish nation that it was God's doing. Stephen's purpose was to prove to Israel that Jesus was the Christ—the prophet like Moses whom God raised up to deliver Israel.

Acts 7:36

He brought them out, after that he had shewed wonders and signs in the land of Egypt, and in the Red sea, and in the wilderness forty years.

Why did Christ have to show wonders and signs to the Jewish nation?

Christ had to show wonders and signs to the Jewish nation to prove that His ministry and works were God's doing. Just as Moses performed signs in Egypt, at the Red Sea, and in the wilderness, these miracles confirmed that Jesus was the Christ and that His power came from God.