Why is Alaska so important to the US?

The question isn't clear if it is asking what the supposed benefits of purchasing Alaska were or if it is asking about general benefits of Alaska over the years. I'll answer the latter.
Alaska is big. When it was purchased, it increased the size of the United States by nearly 20 percent. A gain in territory size is often beneficial to a country because that territory likely contains some kind of financially beneficial resource.
Alaska is rich in gold. Major gold discoveries were made in the Alaskan territory in the 1880s and 1890s.
Alaska has large reserves of petroleum. That petroleum is transported across the state through a pipeline, and the resource is a very valuable commodity to the United States as a fuel source or as a possible product to be exported for profit.
Alaska has a vibrant and robust seafood industry. It creates over 100,000 full time jobs and roughly $5.8 billion in yearly labor income. The economic output of this industry is over $14 billion.
https://ebooks.alaskaseafood.org/ASMI_Seafood_Impacts_Dec2015/pubData/source/ASMI%20Alaska%20Seafood%20Impacts%20Final%20Dec2015%20-%20low%20res.pdf