Tom Riddle's diary is not so much a symbol as a plot point. The diary gives J.K. Rowling an opportunity to bring Harry face to face with the young Voldemort, to start recognizing the similarities between the two, and to affirm his wish to walk a different path. What we like about the diary as a tool to achieve these goals is the way she presents this magical object.
Riddle describes the book as "a memory [...] Preserved in a diary for fifty years" (17.17). Yet he also talks about his possession of Ginny as an exchange of soul:
"So Ginny poured out her soul to me, and her soul happened to be exactly what I wanted [...] I grew powerful [...] Powerful enough to start feeding Miss Weasley a few of my secrets, to start pouring a little of my soul back into her." (17.45)
All of this talk of souls preserved in objects reminds us of something: the Horcruxes of Books 6 and 7. Even though Riddle's diary has a useful plot function in Chamber of Secrets, J.K. Rowling also uses it skillfully to foreshadow future developments about the state of Voldemort's soul and the secret to his continued life after getting hit by a reflected Killing Curse years before. We may not know that the diary is called a Horcrux by Book 2, but we do know that Voldemort has been leaving bits of his soul around – an important point to bear in mind as the series continues.