You ask a simple but profound question. As a word, "faith" comes from the Latin fides, which means "trust." The Greek word is pistis, meaning trust, good faith, trustworthiness. Faith has to do with attitudes of trust, assurance, confidence, reliability, and loyalty to someone or something that we think is worthy and deserving of those sentiments. In Jesus' words: "Where your treasure is, there will your heart be also" (Matthew 6:21). Faith is variously expressed through feelings, beliefs, ideas, customs, commitments, decisions, actions, and a whole way of life.
First, let's take human relationships, where everything stands or falls on faith. A friendship is as strong and durable as the bond of trust between friends. People fall in love and get married. But without faith as mutual trust and trustworthiness, romantic love evaporates, turning into suspicion, jealousy, emotional pain, even hatred. Likewise, a family is customarily bonded by love and loyalty based on blood ties. But without enduring faith and trustworthiness between its members, the family can become quite dysfunctional and fall apart.
The inherent value lies not only in faith as one's personal trust in another but also in the trustworthiness of the other. Human relationships thrive when all parties are faithful, honest, reliable, trustworthy, and committed to each other. The power of faith blossoms in relationship, mutuality, reciprocity. To be sure, an extraordinarily mature and selfless person--whether a friend, spouse, or family member--may well continue to love an unlovable other. But faith as trust and trustworthiness is often diminished and broken by doubt and mistrust if the object of faith proves repeatedly unreliable, dishonest, unfaithful.
On a wider social, political, and economic scale, human relationships are also dependent on mutual "good faith." Society, government, and business are in large measure determined by complex systems of law. Nevertheless, the health and morale of a nation as a whole, and even our world as a family of nations, are very much dependent on basic relationships of faith and trustworthiness exemplified by word and deed. Human beings seemed to be "wired" to relate and act toward each other on the basis of mutual faith and trustworthiness in all areas of life. For this reason, it is all the more important that our leaders in government, law, business, and religion serve as inspiring examples of authentic faith. Apart from faith as trust and trustworthiness, the very fabric of human life is marred by doubt, suspicion, manipulation, and other evils that render social systems ineffective and drive people toward mutual exploitation, conflict, and war.
On the other hand, we believe in God because we trust that God is true, reliable, trustworthy, good, loving, merciful, and, above all, faithful toward humankind. Why so? Because that is the manner in which God has made himself known to chosen witnesses in biblical history. We love God because God has loved us first. We believe in God because God is good and worthy of our trust. We trust and obey God because God is true and reliable. For Christians, the essence of faith as trust and trustworthiness is the person of Jesus Christ, who sums up the "new covenant"--the bond of mutual love and faithfulness between God and his people actualized in daily life according to the principle of "faith working through love" (Galatians 5:6).
What, then, is faith? In simple terms, faith is to trust, accept, rely, and, indeed, stake your life on someone or something as true, right, and good. Faith is influenced by family and community, which often define the content of faith in terms of specific beliefs, customs, ethical teachings, ways of worship, and doctrinal confessions. However, each person's personal faith is often tested by experience, sometimes severely, in which case a "leap of faith" may be required to make the move from cynicism to trust, including trust in God. Saintly men and women of the present and past, by their faith and example, serve as inspirational sparks to our own faith in our existential struggles. Above all, even as we may "walk through the shadow of the valley of death" (Psalm 23:4), we trust in God, who alone can transform our feeble faith into a vibrant and joyful gift embracing all things, including (I might add) nature, which we ought to treat in the same spirit of mutual trust and trustworthiness.