The diary functions as a symbol of Winston’s thoughtcrime, his private revolt against the Party, and of the old times, before the Party came to power, which he is continually trying to recall and discover. He records in writing his hatred for Big Brother and the Party, but even before he writes in it, the book as a physical object (together with the old-fashioned fountain pen he uses to record his thoughts) is already a symbol of everything the Party stands against:

It was a peculiarly beautiful book. Its smooth creamy paper, a little yellowed by age, was of a kind that had not been manufactured for at least forty years past. He could guess, however, that the book was much older than that.

The diary, however, does not only function as a symbol. It plays an important role in the exposition. 1984 is above all a novel of ideas. When the ideas in a novel are paramount, there is always the danger of characters sounding unnatural, as though they are reading from a sermon or a political tract when they speak. Moreover, until he begins talking to Julia, Winston has no one with whom he can share his ideas in any case. The diary therefore functions as a device to allow Winston to think at length without compromising the realism of the novel.

There is irony in Winston's writing in his diary.  There is little doubt that he wrote even one word in the book without someone knowing about it; although this is not known to us when the book starts, we soon realize it must be true.

In terms of the structure of the novel, Orwell uses the diary to involve us in the plot (he does this with another book later in the book when he needs/wishes to convey information [lecture us] about the Emmanuel Goldstein text).  The diary also functions to engage us in Winston's character.  We know that he is not just "another" party member, that he is up to something that we want to know more about.  At the very beginning of the book it gives us some hope that we have here a man whose life may be important; once we learn more about their society, we know that it seals his doom.