Much of the novel's symbolism derives from the books it features. Check out Liesel's "Character Analysis" for lots of discussion on how these books comment symbolically on Liesel, and how book stealing functions as a symbol of resistance against the Nazi regime.
The book burning scene is important to Liesel, but symbolically, it goes beyond her story. First of all, it's a symbol of the countless other book burning in Nazi Germany. It's a bit of a reduction to call these events "book burnings." As the novel indicates, it's not only books being burned, but also art, pamphlets, anything authored by a Jew, or which speaks favorably about Jewish people.
These burnings don't target a single author, or even a single idea, but the collective body of creative and intellectual work of a large group of people. This goes beyond censorship or protest, and it goes beyond books. For the Nazis, Jewish books symbolize Jewish people. The destruction of these books symbolized their goals, the destruction of the Jewish people. The crematoria, chambers where the bodies of Jewish people were incinerated, are notorious. The book burning in the novel reminds us of those crematoria, and helps keep us from getting too comfortable in the story. It also reminds us that Nazi propaganda techniques included destroying information, as well as spreading it.