Follow enough people on Twitter for long enough, and you will become aware of the use of the hashtag. Another of those words that has become common parlance in the last year or so due to the reach of Twitter, the hashtag is a simple enough concept, perhaps best explained by an example: 

Say you have been taking an interest in a news story. For example, the biggest story of 2009 has probably been the death of Michael Jackson. At the time, people who had just heard the news would often finish their tweet with the tag #ripmj or #ripmichaeljackson. By doing this, it flags up the fact that your tweet was about that particular issue. 

Your Twitter homepage will have a list on the right hand side titled "Trending Topics". This is a list of the ten most frequently used phrases or words currently appearing in people's tweets. By clicking on the topic you can see what people are saying about the story. If you have not directly used the words, adding a hashtag at the end means that your tweet will show up in any search using that hashtag. 

The use of hashtags should be approached carefully, however, as many people see it as attention seeking. By using the hashtag, people feel that you are simply trying to get your tweet seen by as many people as possible. Add to this the fact that, if an issue is "trending", then it will be getting tweeted about possibly hundreds of times in a minute - and the chances are no-one but your followers will see it anyway, so think before you use them.