Book burning is a common but controversial way of protesting people's moral or religious objections to things that others have written down. It has been practised throughout history, with the most famous recent example being the Nazi book burnings in Germany in the 1930s and 40s, where around 18,000 different books were labelled "subversive" by the government and huge rallies were held to burn copies of them.
One fictional example of book burning which highlights why many people find it so unpleasant is the book Fahrenheit 451 by Ray Bradbury (from which the opening quotation of this chapter is taken). Here is one scene which deals specifically with censorship.
WARNING: you may find the last minute of this video disturbing.