"'I also established my covenant with them to give them the land of Canaan, where they resided as foreigners. Moreover, I have heard the groaning of the Israelites, whom the Egyptians are enslaving, and I have remembered my covenant.'" NIV translation
Because of God's previous promise (covenant) with Abraham, He not only heard their cry but also was ready to take action on their behalf. God is reminding Moses of the past so that he can be completely sure of the future things that are being revealed to him. This is the biblical principle of building faith through experience. Faith (trust) is built when we see promises fulfilled.
Based on the covenant of the past, God promised complete deliverance for His people. We remember that the number seven refers to completeness and this verse begins seven "I will"s where God gives specific promises concerning the deliverance. The "I will"s are a reminder that it is God that does all of the work of deliverance.
The same thing is true for us as Christians. No matter what we are looking to be freed from, it is only the power of God that can accomplish the task.
"'I will take you as my own people, and I will be your God. Then you will know that I am the Lord your God, who brought you out from under the yoke of the Egyptians. And I will bring you to the land I swore with uplifted hand to give Abraham, to Isaac and to Jacob, I will give it to you as a possession. I am the Lord.'" NIV translation
Moses is to reassure the Israelites that God will be with them every step of the way and that He is not redeeming them just to abandon them later. The same is true for us today as He delivers us from our sins and from our struggles. He does not leave us where we were but leads us on to grow closer to Him and to know that He is with us every step of the way.