Topics can be useful on their own to build small vignettes with words that are in the previous screenshot. These visualizations could be used to navigate a large collection of documents and, in fact, they have been used in just this way.
However, topics are often just an intermediate tool to another end. Now that we have an estimate for each document about how much of that document comes from each topic, we can compare the documents in topic space. This simply means that instead of comparing word per word, we say that two documents are similar if they talk about the same topics.
This can be very powerful, as two text documents that share a few words may actually refer to the same topic. They may just refer to it using different constructions (for example, one may say the President of the United States while the other will use the name Barack Obama).
