A YouTuber is a person who has an account on YouTube, and views YouTube.com's many videos. If they like, they may comment on the video, rate a video, (used to be five star rating, but now it's like or dislike), and makes YouTube videos themselves. Users used to be able to post video resposnes underneath of people's videos, but as of 2012, YouTube got rid of that feature.
YouTube celebrities are people or groups who are popular because of their videos on YouTube. Some of them have corporate sponsors, who pay for product placement in their clips or production of online ads. Some YouTubers have even become famous in the media. Canadian singer, Justin Bieber (kidrauhl) was discovered on YouTube and became one of the world's biggest superstars at only 15 years old.
YouTube Partners are YouTubers who make money off of the videos they make on YouTube. In the early days there was only YouTube/Google Ad Sense, which gave the uploader a little bit of money whenever a viewer clicked on the ads on their videos; however, as of 2010/2011, third party partnership programs have shown up to partner specific YouTuber that make specific content; although not all of them, many of these YouTubers have found a way to make a living off of their partnerships, which is known to be impossible with normal ad sense.