This is a tough question because Goodman Brown doesn't explicitly declare his purposes for going out into the woods that night.  The reader is left to make his/her own judgment.  The text does give some insight though.  

"My love and my Faith," replied young Goodman Brown, "of all nights in the year, this one night must I tarry away from thee. My journey, as thou callest it, forth and back again, must needs be done 'twixt now and sunrise." 

The above quote doesn't really give an indication as to why Brown agrees to the meeting in the first place; however, the quote does emphasize that Brown's meeting had to happen that night. For some reason, the meeting is time sensitive.  

Additionally, the meeting is important to Goodman.  He may not know exactly what the meeting will entail, but his wife, Faith, begs him to not go.  

"Dearest heart," whispered she, softly and rather sadly, when her lips were close to his ear, "prithee put off your journey until sunrise and sleep in your own bed to-night. A lone woman is troubled with such dreams and such thoughts that she's afeard of herself sometimes. Pray tarry with me this night, dear husband, of all nights in the year."

Brown has been married for three months, and his lovely wife is begging him to stay home with her.  Whatever Goodman's purpose for the meeting is, it has an extremely strong pull over him.  

While Brown might not know exactly what his meeting is about, he does know that his meeting is not acceptable for a Puritan man of faith to attend.  

With this excellent resolve for the future, Goodman Brown felt himself justified in making more haste on his present evil purpose.

As a Christian, Goodman Brown knows about the presence and power of good and evil in the world.  He is very aware of Satan's power, and he knows that eternal damnation is a possible outcome of making deals with the Devil.  You could surmise that, despite knowing all of that, Goodman Brown feels confident in his own spiritual strength.  I think that is part of why he goes into the forest for his meeting.  I think that Goodman Brown truly believes that he has a strong enough faith to resist any temptation that Satan gives him.  

It turns out that Brown is correct too.  Satan does not turn Goodman Brown.  He doesn't become a Satan follower.  Brown's faith wound up being strong enough; however, Satan was still able to destroy Brown.  Goodman Brown might not have turned to Satan, but he lost his faith in everybody else . . . including his wife.   

When the minister spoke from the pulpit with power and fervid eloquence, and, with his hand on the open Bible, of the sacred truths of our religion, and of saint-like lives and triumphant deaths, and of future bliss or misery unutterable, then did Goodman Brown turn pale, dreading lest the roof should thunder down upon the gray blasphemer and his hearers. Often, waking suddenly at midnight, he shrank from the bosom of Faith; and at morning or eventide, when the family knelt down at prayer, he scowled and muttered to himself, and gazed sternly at his wife, and turned away.

I said that Goodman Brown's belief that he is strong enough to resist the Devil is only part of why he goes to the meeting.  I think the other part of the reason is pure curiosity.  Curiosity is a difficult temptation to resist, and it appears that Brown was not strong enough to resist the pull of curiosity.  He just figured that he is strong enough and in control enough to appease his curiosity, walk away unaffected, and return to his wife by morning.  

That's the situational irony! A good man who believes in the Christian god like the Puritans did shouldn't be going out to meet Satan. However, it is even more ironic that he sees other town's folk meeting with Satan, too, which then pulls down his faith at the same time.  It can be argued that young Brown justifies his meeting because he will be back to his wife in the morning.  He's merely going to check things out, but he is a loyal husband and knows that he will still be loyal after this meeting.  Curiosity gets to us all, it seems, because he thought that he was in control of the situation, but is then very much disappointed and confused at what he discovers.  All of the people that he looks up to are there, and this challenges his own belief, which eventually takes away his faith in anyone or anything for the rest of his life.