Comment rating can have many uses. First and foremost is a way to discourage bad behavior when posting. Trusted Users are allowed to 'zero' comments, and thus hide those comments from other readers. Because no moderation system is perfect, other trusted users can view the hidden comments and un-hide the comment if it isn't so bad. Thus, low rated comments tend to be inflammatory or trollish and anti-community or just obnoxious. However, don't feel that when rating comments you have to go along with how everyone else moderated the comment.
A second use for the rating is editorial, to indicate whether or not the comment is well-written, well-reasoned, informative, etc. Ratings are also used to show appreciation for a given comment. Often this is when someone posts something insightful or funny, people will rate the comment a 4. Some people rate a comment in their diary as a "thanks for contributing" signifier. Others don't rate comments, or rate everything down the middle.
It is generally considered bad form to write a diary or Posting Comments to complain about a rating someone gave you. If you received a low rating, you should ask yourself what you did to get such a response, and abstain from doing it again. It's also bad form to rate in vengeance, or to "modstorm" users. You should avoid giving low ratings to people who reply to you except in the most extreme cases.
Creating secondary accounts to rate your own comments is considered abuse and can result in deletion of the comments in question.
As seen in User Preferences, you can set your ability to rate, whether ratings are displayed, or how comments are displayed according to ratings, as well as the ratings button or dropdown list appears.