Using hashtags on Twitter allows users to categorize their Tweets [Twitter updates]. If you click on that #word, you will see all of the recent Tweets that include #word.
The Twitter help center explains in What Are Hashtags ("#" Symbols)? that the symbol "is used to mark keywords or topics in a Tweet. It was created organically by Twitter users as a way to categorize messages."
[Note: you'll enjoy this article titled The Short and Illustrious History of Twitter #Hashtags.]
The article includes best practices for using hashtags: no more than 3 hashtags in a Tweet [I recommend no more than two] and be relevant when using one. It also refers to the Twitter Fan Wiki page on Hashtags which includes not only great advice on using hashtags on Twitter, but also a comprehensive list of further reading on hashtags.
Hashtags exist on a multitude of topics. If you don't believe me, check out hashtags.org and go explore.
I came up with the following 11 reasons for using hashtags on Twitter:
1. For a Twitter chat [see How Do I Twitter Chat]
2. To monitor trending topics [see Women's World Cup Final Sets Twitter Record]
3. To communicate during emergencies [e.g., 2007 California Wildfires]
4. To monitor conferences even from afar! [see I attended NeoCon... Virtually!]
5. To share related links and articles [see my #retailexp and #practicalmktr tweet roundup posts]
6. For sharing notes or asking questions during webinars or online seminars [e.g, #mprofspro]
7. To capture a mood [for a while I was tracking #simplepleasures]
8. To celebrate Friday [#FF or #FollowFriday] or Monday [#MarketerMonday] or Tuesday [#TileTuesday or #TravelTuesday] or...
9. To signal - for example #quote, #jobs, #sale or #Coupon
10. As a reminder: #ToDo
11. As part of a promotion [see Tigressa SoftStyle Carpet From Shaw...]
What other reasons can you think of for using hashtags on Twitter? Let me know in the comments.
PS: You might enjoy The Power of Hashtags on Twitter which refers to hashtags as the "World's chat room".