The Greek word translated as "faithfulness" in this passage (πίστις) is most often translated simply as the word "faith." That's because faithfulness is all about having faith. The object of our Holy Spirit-given faith is, well, God. That's because God is the only one we can completely trust with every aspect of our lives.
So do not worry, saying, 'What shall we eat?' or 'What shall we drink?' or 'What shall we wear?' For the pagans run after all these things, and your heavenly Father knows that you need them. But seek first his kingdom and his righteousness, and all these things will be given to you as well. (Matthew 6:31-33 NIV)
Most of us worry about things like what we will eat, where we will sleep, and what we will wear. In our culture, we not only worry about meeting these needs at the most basic level. We pursue these area far beyond what we need to survive. We like only certain types of foods, we crave a certain type of home, and we buy clothing that matches the right kind of fashion (for me that fashion is stuck in the 80's). We don't really know how to not worry about or pursue these things. It's a part of our upbringing, our everyday conversations, our way of life.
When Jesus trained his twelve apostles, he was preparing them to fulfill his final command before ascending into heaven: "Go and make disciples of all nations..." That training included some practice runs, where they would learn God's system for providing for their food, clothing, and shelter. They would be paid by the people they teach. This would be God's way of providing for them. When Jesus taught them this process and sent them out to practice, he did it, in part, to build their faith. They needed to know that God's plan for their lives would provide for their needs. It helped them become people full of faith in God - faithful to His plan.
The elder, To my dear friend Gaius, whom I love in the truth. Dear friend, I pray that you may enjoy good health and that all may go well with you, even as your soul is getting along well. It gave me great joy when some believers came and testified about your faithfulness to the truth, telling how you continue to walk in it. I have no greater joy than to hear that my children are walking in the truth. Dear friend, you are faithful in what you are doing for the brothers and sisters, even though they are strangers to you. (3 John 1:1-5 NIV)
Many people besides the twelve lived a faithful life in first century Christendom. Many people have lived faithfully throughout history. Many still live faithfully today. We live out our faith in God to provide for our needs as we participate in His plan. We do our part trusting God to do His. As we are filled with faith in God, God shows Himself to be worthy of our faith.
So, how about you? Do you have faith in God? Do you trust God with every area of your life? Are you filled with faith? Would you consider yourself faithful?