A rival is a competitor or contender that you want to defeat, whether in an actual competition or for another goal. It may be a tennis rival or a rival for your true love’s affections.
There are all types of rivals, but they tend to show up a lot in sports. For example, in college football, the Army and Navy have been rivals since their first meeting in 1890. Something that is able to rival something else is seen as comparable to it in quality, and something that is said to be “without rival” is unmatched, or better than everything else.