What is in the briefcase that the man gives to Winston, and why is this item of special importance?

In Part Two, Chapter Eight, O'Brien arranges to give Winston a briefcase:

At some time during the day, in the street, a man will touch you on the arm and say “I think you have dropped your brief-case.” The one he gives you will contain a copy of Goldstein’s book. You will return it within fourteen days.

As arranged, Winston receives the briefcase the day before Hate Week begins but is so busy that he is unable to open it immediately and look at its contents.

The significance of this briefcase cannot be overstated. Inside, it contains a copy of "the book," penned by Goldstein, an enemy of the party. This book contains the truth about the party's hold on the people of Oceania and explains how they use war as a means of manipulating and controlling the people. 

Receiving the briefcase, then, is symbolic of Winston's open state of rebellion. He has outed himself to O'Brien and voiced his anti-party sentiments. Receiving the briefcase is representative of his commitment to the resistance movement and his desire to overthrow Big Brother and create a new society.

In an ironic twist, however, it is later revealed that this was all a ruse. O'Brien is, in fact, a senior member of the Thought Police who has used the briefcase to detect Winston's thoughtcrime. So, while the briefcase came to symbolise Winston's freedom from the party's control, it now becomes the symbol of his downfall. In Part Two, Chapter Ten, the briefcase and the book lead directly to his arrest and his torture at the hands of O'Brien.