We remove posts in order for them not to be seen by others. This includes very low quality posts, for example when a post is filled with characters from the number row of your keyboard with Shift pressed. It is restricted to posts which are beyond saving; the user has made it clear that he is not going to edit the post to make it fit. Also note that some of these answers are converted to comments rather than deleted.
This is censorship in the sense that garbage is removed so that they cannot be read. That is a service to the community. It is not censorship in the sense that moderators remove posts because they disagree, don't follow some "agenda", etc.
In less clear cases, I usually leave a comment explaining why the post doesn't fit (for example when a new user adds a new question as an answer).
I don't have data on how many posts are deleted on other sites.
I have recently been thinking about a system where we can keep a public list of deleted posts, which cannot be commented / voted on - just to be fully transparent. However, we wouldn't want to include the most mundane language in that "trashcan", to not give spammers a podium. So there should always be an option to not include a post in that public trashcan, hence I don't expect this will take away all (if any) doubts.