Censoring removes material from a work; deleting a scene, placing black bars over exposed genitalia, "bleeping out" obscenities, and so forth. For example, Pink Floyd's song Money had a censored version for radio play throughout most of the 80s and 90s where the line "Don't give me that do-goody-good bullshit" had the word "shit" replaced with silence.
Moderating in internet usage is often a combination of editing and censoring; you look over existing posts for offensive or off-topic material and either re-word the offensive parts or remove the posts. Preferably there is an element of feedback in this process to provide the offending poster with a chance to improve their habits.
The other type of moderating generally is as the person who facilitates a debate between two or more people, making sure that all debaters get asked the same questions, get the same chance to answer them, and do not monopolize the microphone.
Reviewing is providing feedback regarding a work (sometimes directly to the author, sometimes to the potential audience of the work), where you explain what you liked and didn't like about it, and in the case of direct feedback given prior to the work's final production, make suggestions on how to change the work to improve it. For example, Many authors provide pre-release copies of their latest book in a series to a small core of dedicated fans, who point out problems with continuity, plot holes, and the like so that the author can fix things up before the book is published.