Most books of the Bible have come down to us with authorship well-established. The first four books of the New Testament are titled by the names of their authors (Matthew, Mark, Luke, John). And most of the letters from Paul actually state internally that they came from the great Apostle. But Hebrews is different. It starts right out into logical argument, and never identifies the author.
There are many theories as to the writer, which are worth checking out. The majority views tend to be either Paul, Barnabus, Silas, or some other student of Paul transcribing the apostle's thoughts into his/her own words.
Is it important who the author is? Yes and no. It is good to know the authorship to understand the writer's motivations, background, and context. But it is not necessary as the early church applied strict rules to which books made it into the scriptural canon, and can be trusted to have made sure this letter - like the others in the Bible - came from someone who knew Jesus and was a true Christian.