What were the possible reasons for Brown taking such a night's journey?

Hawthorne's story initially obscures the purpose and nature of the journey. Brown states to his wife:

My journey, as thou callest it, forth and back again, must needs be done 'twixt now and sunrise. 

This image of an urgent journey which must be done under the cover of darkness, the nature of which is not initially shared with Faith or readers of the story, creates suspense. We read on to discover what the errand is...

Hawthorne's story initially obscures the purpose and nature of the journey. Brown states to his wife:

My journey, as thou callest it, forth and back again, must needs be done 'twixt now and sunrise. 

This image of an urgent journey which must be done under the cover of darkness, the nature of which is not initially shared with Faith or readers of the story, creates suspense. We read on to discover what the errand is and why Brown must do it.

We immediately discover that Brown thinks of the errand as having an "evil purpose." As he meets with the mysterious shadowy figure who guides him, he states his belief that the evil in which he is participating is one that neither his family, nor his community would countenance, a statement that is disproven when he finds the entire town, including his wife, participating in dark rituals in the woods. 

His purpose is not directly stated, but, as this is a strongly religious story, we should view it theologically. It seems that curiosity is a driving force as is the influence of the Devil. Given the Puritan background of the story, we can argue that all men are naturally susceptible to temptation (and are fallen due to Original Sin). Salvation is only possible through faith, and yet, in rejecting Faith's request that he not go on the journey, Brown gives up his one defense against the inherent fallen nature of humanity and thus falls prey to the Devil.