The nobleman asked Jesus for healing, and Jesus proclaimed healing without the nobleman actually seeing the healing take place. But even with the lack of information on if the son got healed, the nobleman trusted Jesus. He trusted Jesus even though all the nobleman had was prior knowledge of Jesus as well as a statement (not a sight).
While the nobleman went his way, his servants proclaimed that his son did indeed get healed! And when the nobleman asked when the son got healed, the servants replied that it was at the seventh hour -- which was exactly the time when Jesus proclaimed that the son got healed. Indeed, the nobleman found another reason to believe in Jesus and that Jesus works -- even without being in the same room! The healing was another sign Jesus did, but it was out of sight.
Jesus does all sorts of works, but because many of his works are out of sight or at different timing, we sometimes need to trust his word. However, we can trust in Jesus because of what he has done beforehand.