I generally think that it is ridiculous for a company to advertise a product as "New and Improved." Usually, something must be either one or the other. If a product is new, then it hasn't been around to be improved. And if a product has been improved, then it has already been around for a while and must not be new. But in Hebrews 8, God presents us with a covenant that He says is new. But God also contrasts that covenant with an older covenant and shows that the new is an improvement.
The Old Covenant was the law of Moses. It was a deal that God made with the people of Israel that was based on them obeying the 613 laws that were given. When a law was broken, a sacrifice had to be made. But the New Covenant (also made with the people of Israel) is much better because the New Covenant is internal and people want to follow it. People are able to follow the New Covenant, but they were unable to follow the Old. The requirement of the New Covenant is faith in Jesus Christ. HIs perfect sacrfice for sin fulfilled all of the sacrifices of the Old Covenant. Therefore, not only is the New Covenant an improvement over the Old Covenant, but Jesus is seen to be the best (and now only) way to approach God.
Since Jesus is the best way to God, we ought to come to God through Jesus. And since Jesus is great, we ought to rely on Him for help in everything that we do. The greatness of Christ can give us a tremendous assurance of God's love. The greatness of Christ can also give us additional reasons to trust Him to guide us through every situation of our lives.