There are two ways that I think about this word in the Christian context. First, the penalty for sin has been satisfied by the sacrifice of Jesus on the cross. Second, as believers, we can be satisfied with the new life we have in Christ.
On the first point. The fullness of sin has been dealt with by the abundance of Jesus’s righteousness. And God, through his grace, has applied that righteousness to our account. We are no longer under condemnation because the holy wrath of God has been propitiated by the blood. This is what it means for God to be satisfied by Jesus’s sacrifice for my sin.
On the second point. Now that I have been born again through repentance and faith, adopted into the family of God, and the righteousness of Christ covers my sin, I can live a satisfied life. This is not a complacent life. It is not a careless life. It is not a hesitant life. I don’t have to live in fear, but I do have to live for God. It is an intentional approach to life. My satisfaction is not in trying to do what Jesus has already done. My satisfaction comes when I live my life in accordance with God’s character. The only perfection God expects he has found in his Son. What he wants from me, from you, is a commitment to faithfully obey his commands.