Who was the author? To be perfectly honest, we don't know who the Holy Spirit inspired the book of Hebrews through. Some say Paul, others Timothy, still others Barnabas, and yet others (including Martin Luther) Apollos. The lack of an identified or widely-accepted author may be one of the reasons why some spoke against including the book in the canon of Holy Scripture.
What is the book? The book was probably more of a sermon than an apostolic letter. Either way, the target audience was likely in Rome, where Jewish Christians (thus "Hebrews") were strongly tempted to revert to Judaism in order to avoid persecution.
Where was it written? Identifying where the book was written is tied up in identifying its author. If a sermon, then the "book" was likely recorded in Rome; if a letter, then the location from where it was written depends at least in part on whom one identifies as its human author.
When was it written? Given that persecution was on the increase in Rome and that the Temple in Jerusalem seems to still have been in use, the usual range of dates for the writing of the book is from A.D. 65-70.
Why? As indicated, the original hearers were being tempted to return to Judaism to avoid persecution, so the author tries to convince them of Christianity's superiority. We may be far less tempted to practice Judaism, but that doesn't mean the letter isn't relevant for us.
How? The author emphasizes Jesus's humanity and His work as our all-sufficient Prophet, Priest, and King. The author is well aware that his original hearers were-as we are-living in the world's final days, and that urgency drives the exhortations of the book.
For further reading on the book of Hebrews:
- Luther, Martin. "Lectures on Hebrews" (1517-1518). Vol. 29, pp.107-241, of Luther's Works, American Edition, eds. Jaroslav Pelikan and Walter A. Hansen; tr. Walter A. Hansen. St. Louis: Concordia Publishing House, 1968. (There are some interesting comments by the "young" Luther, although the comments only go through Hebrews 11. You can find this volume in our Grace library.)
- Westcott, Brooke Foss. The Epistle to the Hebrews: The Greek Text with Notes and Essays, second edition. New York: Macmillan and Co., 1892. (I have a number of Hebrews commentaries, and this is my favorite, although it is more than a century old. You are welcome to borrow the volume, but know that it is quite scholarly, with a heavy emphasis on the Greek and passages quoted in German and Latin.)
The Concordia Commentary series has a volume forthcoming on Hebrews, authored by the present president of the seminary from which I graduated.