What is the importance of Marlowe's Doctor Faustus and why?
This is almost a trick question. There are many considerations that might make a play "important": religious considerations, historical ones, literary ones, personal ones, biographical ones. The Tragical History of Doctor Faustus might be called important for reasons from any or all of the categories above. Let's sort some of it out.
Doctor Faustus is considered important as it is Christopher Marlowe's greatest play and masterpiece. While Marlowe made great contributions to theater in England during his turbulent and brief career as a playwright, such as introducing blank verse to English drama in Tamburlaine, Faustus continues to be a masterpiece of interest even till today. It is the play that most immortalizes Marlowe's name and work.
Faustus deals in a most controversial way (audiences are said to have been terrified and to have believed the Devil had actually visited the theater) with religious issues and issues of faith during an era when religion and faith were undergoing upheaval in the wake of Luther's Reformation. Therefore religious importance is attached to Doctor Faustus. It gives a contemporaneous view of some of the issues of faith and religion that were current at the time it was written, for instance, how one was to claim and receive repentance and forgiveness:
FAUSTUS: Hell strives with grace for conquest in my breast:
What shall I do to shun the snares of death?
See, see, where Christ's blood streams in the firmament!
One drop would save my soul, half a drop: ah, my Christ!—
These are two significant ways in which Doctor Faustus may be considered important. Others might be discovered by reading Marlowe's biography and by considering the effect the play has on individuals past and present.