What did God want Israel to believe when Moses showed them signs?
God wanted Israel to believe that the God of their fathers—the God of Abraham, Isaac, and Jacob—had appeared to Moses. The signs, the rod becoming a serpent and the hand becoming leprous and then whole, were given to prove to Israel that Moses was God’s man.
Les explains that God sent Moses back to the people under slavery in Egypt and told him that if they did not believe him, he should throw the rod on the ground, and it would become a serpent; when he picked it up, it would become his rod again. God also gave another sign: Moses put his hand in, and it became leprous; he took it out, and it was perfectly whole as before. Verse 5 gives the purpose: "that they may believe that the God of their fathers, the God of Abraham, Isaac, and Jacob, hath appeared unto thee." These signs were given to Moses to prove to Israel that he was God's man. Les also notes that Israel was used to such supernatural workings because they happened throughout their history.