Jesus made the bold claim that He was God. He was persecuted because of that claim. Really, anyone can make that claim. But that leads to the question, "where's the proof?"
In Jesus' case there are many proofs. John wrote his Gospel to record just some of those proofs.
A sign is a distinguishing mark by which something is known. Jesus gave many signs or miracles. His apostle John did not choose to include in his gospel account all of Jesus' signs. But he did select seven that he wanted the reader to get a handle on.