The importance depends on how you value some of our impact in the world. Some people say that life makes no sense if in the end you will be destroyed and disappear forever. I can see that in this scenario, individualism, egotism, and things like these are senseless. But not necessarily life. Humanity as a whole is writing a history in the world. As long as this story continues, we have an impact and our legacies will persist. Memories about us will also persist, specially if you define "memory" as information stored somewhere, not necessarily in a brain, and not necessarily intact and imutable.
About the nihilism that in the end everything will be destroyed... Well, there is a part in the bible where someone says that there are never something new under the sun. Our struggles are equal the struggles that someone before had. Our problems are equal the problems that someone already had in the past. And everything that we do is irrelevant in the end. Which is false, and for us that have access to studies in history, we can easily see that is false. We have new problems in modern times. Our development also turned us less irrelevant. While still astronomically minuscule, we are not anymore worldly minuscule. We have power to change the climate in the entire planet, we can even destroy most life and even ourselves with our technology, we are beginning to explore other worlds. What is the limit? It is unknown. If in the antique world it was easy to be mistaken thinking that the limits that they had were the definitive human limits, why wouldn't be also easy for us being wrong thinking that the limits that we currently have are definitive? Yes, now we have limits on how could we deal with the destruction of our solar system. But we could in the future learn how to survive this. We do not know and never will know what is the limit for what we can achieve. Therefore, believing that all is senseless because our limits will trap us in a dead end is a not very useful unbased claim. This is a case where Pascal's wager makes sense: if indeed we will be unavoidably trapped in a dead end, you lose nothing thinking that there is a way to avoid this, but if we are able to escape the dead end and extinction, it is deleterious to believe that the extinction is unavoidable.
About the nihilism that in the end everything will be destroyed... Well, there is a part in the bible where someone says that there are never something new under the sun. Our struggles are equal the struggles that someone before had. Our problems are equal the problems that someone already had in the past. And everything that we do is irrelevant in the end. Which is false, and for us that have access to studies in history, we can easily see that is false. We have new problems in modern times. Our development also turned us less irrelevant. While still astronomically minuscule, we are not anymore worldly minuscule. We have power to change the climate in the entire planet, we can even destroy most life and even ourselves with our technology, we are beginning to explore other worlds. What is the limit? It is unknown. If in the antique world it was easy to be mistaken thinking that the limits that they had were the definitive human limits, why wouldn't be also easy for us being wrong thinking that the limits that we currently have are definitive? Yes, now we have limits on how could we deal with the destruction of our solar system. But we could in the future learn how to survive this. We do not know and never will know what is the limit for what we can achieve. Therefore, believing that all is senseless because our limits will trap us in a dead end is a not very useful unbased claim. This is a case where Pascal's wager makes sense: if indeed we will be unavoidably trapped in a dead end, you lose nothing thinking that there is a way to avoid this, but if we are able to escape the dead end and extinction, it is deleterious to believe that the extinction is unavoidable.