What does mean by "faith" here? The word "faith" in this verse comes from the Greek word πίστις or pistis. πίστις means to rely upon someone. Thus, being faithful means trusting completely. Being faithful means having complete confidence. Being faithful means trusting not in our physical eyes, but in our heart that God exists and He is there for us.
This situation and statement by Jesus indicates that the key requirement of Jesus’ healings was reliance upon God. Jesus simply wanted to teach those around him to trust and rely on God. The actual healings are not the message of Jesus. His healings were meant simply to demonstrate our need to rely upon God.
The only way that Jesus could have any power to heal was through his determined reliance upon God. As Jesus demonstrated repeatedly, Jesus' power and authority came from God. This means that Jesus relied upon God for this authority and power. He was God’s instrument. He was not God Himself, however. He worked on behalf of God. We should remember Jesus' prayer:
"My Father, if it is possible, may this cup be taken from me. Yet not as I will, but as you will." (Matt. 26:39)
This clearly indicates that Jesus was not God (why would God pray to Himself?), and Jesus' intention to do God's will and not his own will. Jesus wasn't out to glorify himself. Jesus wasn't trying to prove that he was great. He was trying to prove that God was great, and that we, too, can rely upon God.
It is specifically for this reason that people often confuse God and Jesus. A person who commits to someone and becomes authorized by that person to speak on behalf of them becomes that person’s representative. If an ambassador of a country makes an official statement to a foreign government official, for example, that statement is understood to have come from the leader of the government the ambassador represents.
In the same way, should a servant of God offer his life and surrender to God, God may empower that person to represent Him. Upon this, the statements of the servant will now reflect the instructions of God.
While we might ceremoniously and sentimentally praise Jesus in church in different ways, these statements have no meaning unless they accompany following Jesus' teachings. His teachings were simple: Have faith in God. Love God. Give our life to God. This teaching is simple, yet difficult to practice - because most of us love ourselves just a little too much.
The physical world was set up by God for those who do not want to love Him or serve Him. This started when we first rejected God in His kingdom. So He sent us down here to the physical world, and we took on temporary physical bodies (The Lord God made garments of skin for Adam and his wife and clothed them. (Genesis 3:21)). These bodies, and the identities associated with them are temporary. They are not our true identities. We were thrown out of the place where we were our true identities (So the Lord God banished him from the Garden of Eden to work the ground (Genesis 3:23)).
Furthermore, God set up the physical world to be a place where we cannot see God with these physical eyes (unless God specifically allows it). In other words, while in physical bodies, we do not have to face God. We can pretend to hide from God. We can pretend He does not exist. Although it is not possible to really hide from God, we are given the opportunity to ignore God. This gives us the freedom to choose Him or not. It gives us the opportunity to ignore Him. Or not. We have the choice. If He were visible to our physical eyes, then we could hardly ignore Him or make a choice, could we?
In other words, the world is set up so that we have the freedom to choose whether we want to love God or not - because love by definition requires freedom. We can instead focus our love upon ourselves, and those temporary material assets like money, family, wealth, prestige, power, and so on. Or we can decide that we want to have a relationship with God.
Not only does this temporary world give us the freedom to choose God or not, but this world is set up to test our faith should we begin to choose God.
God does not want us to choose Him whimsically. He wants us to be serious about Him. Therefore, for those who make some effort to know Him, He has created various barriers (illusions of potential material happiness) in order to test us. This is because He wants us to be sincere.
Any relationship requires sincerity. If a boy whimsically asks a girlfriend to marry her without obvious sincerity, would the girl immediately say yes? Only a stupid girl would marry a boy who was not sincere.
And what would the girl do if she wanted to marry the boy did not feel he was sincere? She would probably begin to test that sincerity, in the hopes that if he wasn't sincere, over time he might become sincere.
This is precisely what God does. His physical world tests our faith by throwing all kinds of doubts and temptations at us. He also continues to hide from us, revealing Himself only as we become sincere.
This testing of our sincerity and faith in God is precisely why we have modern scientists coming up with theories of how the universe came to be by accident. This is why there is sexual attraction. This is why there are dreams, television, fantasy, and the illusion of power. These are all set up to either draw us away from Him (for those of us who choose not to be with Him) or test our resolve to return to Him.
Should we endure the challenges of the physical world and maintain our steadfast faith in Him - even if we may fall occasionally and fail some tests - we will undoubtedly return to our eternal relationship with Him. This is because God is loving and merciful, and wants us back.