When postage stamps were first issued in the 1840s, different designs were only used to distinguish between the values represented. It wasn't until the late 19th century, for the 400th anniversary of Columbus landing on the American continent, that the Post Office specifically produced a stamp to commemorate an occasion. However, since then, the creation of stamps remembrance of significant events and people has become common practice. These stamps are popular with collectors because they are only printed for a limited time, which reduces the number of stamps in circulation.
Many stamp collectors, or philatelists, make an effort to buy commemorative stamps as soon as they are issued, so that they are never used and remain in mint condition in a collection which may be handed down over generations. But others are more intrigued by seeking out history that's still available today.
Rare or old stamps
Collectors often have an interest in stamps that are hard to find, so hobbyists who pursue commemorative stamps seek certain old or rare issues to add to their collections. The stamps which commemorated Columbus, issued in 1892 in a series of 15, are worth more than they were at the time, for instance.
However, it is the "error" stamps of that run that are truly valuable. For instance, some of the 4¢ Columbus stamps were accidentally printed in blue, which has increased their current worth to tens of thousands of dollars due to their uniqueness.
Topicals
Another interest philatelists have is collecting postage that is particular to a theme. Commemorative stamps are a great method to help carve out a topic within the enormous world of stamp collecting. People might collect stamps which memorialize great women, or commemorate war, or celebrate authors.
Whatever the theme, there are commemorative stamps relevant to it. Some are valuable, some are rare but all are enjoyable to collect.