Hashtags are often used on Twitter and Facebook. They also appear on Instagram. Sometimes a person will say the word "hashtag" out loud, followed by an oral tag. They are dorks and should be ignored. Here are some examples from Twitter:
Thank you, Statue of Liberty, for always lighting the way to freedom, truth, and yes, even New Jersey. http://t.co/73ax1FFFRb #ThankYouNotes
— Late Night (@LateNightJimmy) December 14, 2013
Gah! Taking notes from the college plays...and throwing in to retro Steelers tricks! I love Troy. #SteelersNationYou can identify it by its preceding "#" You may recognize this as the "number sign," or the pound key on your phone. In press releases "###" signifies the end.
— Kayleigh Elizabeth (@kayleidoscope) December 8, 2013
Hashtags can appear anywhere, but are commonly used at the end of the missive. On Twitter, popular hashtags are turned into "Trending Topics." (Some of the topics are paid for by sponsors.)
If you click the hashtag—the whole phrase with the pound sign—you will see all updates with that hashtag on the network. This is what happened when I clicked "#Caps"
Before I send you into that tagged world, some tips on using hashtags yourself:
It is considered bad form to use too many hashtags in a post. Consider limiting it to no more than three, though one is probably best. Make sure your hashtag is an identifier (like in the examples above) and/or the subject of your tweet. Moreover, make sure it is specific. (Don't use #art when #sculpture would be better.) Finally, your hashtag must be relevant.
Using hashtags on Twitter, Twitter Help Center
How do I use hashtags?, Facebook