One of the very important implications of the covenants we discover in the Bible is that God (YHWH) is different from the gods of the pagans. People imagined these gods to be fickle, cruel, mean, and unreliable. They could not be trusted, for they were really nothing more than super humans using people as pawns in their sadistic games. YHWH, the covenant making God of the Bible, is different. He can be trusted and He has a desire for people to succeed. Think about that reality for a moment. When we have a covenant relationship with God He has a great desire for us to succeed! We don't have to be fearful that God is looking for a reason to punish us, rather we can go boldly go to our Father in Heaven and ask for the wisdom, the strength, and the support we need to live the life He created us to live. Ultimately knowing that we are in a covenant relationship with God means we can trust God to help along the way.
Another very important implication of covenants is that in them we discover the expectations God has for people. In other words we discover what it looks like to be faithful. To be faithful doesn't mean that I will continue to have a belief that God exists, but rather that I remain true to who God is. My marriage is based, not on the fact I believe my wife exists, but my love, loyalty, and service to her. To be in a covenant relationship with God means that He has clearly explained, in the terms of the covenant, what is looks like to be faithful to Him. We don't have to guess what we have to do.
A third important implication of covenants, and especially in being in a covenant relationship with God, is that we can be secure and confident in that relationship. A covenant relationship reaffirms that our salvation is not based on what we do, but is based on God lovingkindness. He is the one that took the initiative to save us, and He has promised to help us along the way.
Covenants are not incidental to our theology, but they are at the very foundation of it. Yes we have a personal relationship with God, but that personal relationship is based on covenant. I think the more we understand about covenants, especially the New Covenant God established through the death and resurrection of Jesus, the more confident and hopeful we will be in our relationship with Him.