What does Genesis 6:18 mean?
The prior verse summarized God's plan to wipe out all land-dwelling life on earth with a flood. Before that, God had given Noah instructions on building the huge ark which would carry man and animals to be spared. Here, God specifically tells Noah that he and his family alone would be saved from the flood.In doing so, God uses a word which will become important for God's people forever: covenant. This term implies more than just a simple contract, or agreement. It carries the idea of a pledge and a promise. God says that He will establish His covenant with Noah. In this case, God wants Noah to understand that the Lord is obligating Himself to save Noah and his family from the coming destruction.
The purpose of God using this language is trust. A covenant is a very solemn, serious obligation. Its worth is only as good as the person making it. At the same time, it implies that the one making the covenant is staking their entire reputation on upholding their end of the bargain. So, when God tells Noah He is making a covenant with him, it implies the most absolutely binding, serious kind of commitment. If Noah cannot place his trust in a covenant from God, he can't place his trust in anything.
God's covenant with Noah—and through Noah with humanity to follow—will be further developed in the coming chapters.