Although the use of a hashtag has been a huge part of the social media marketing world for a few years now, solely to Twitter. The hashtag is a tool to "mark keywords" through the social media site. It creates a category for similar thoughts.
For instance, live tweeting at an event and adding a similar hashtag (i.e., #SXSW2013, or #GrammyRedCarpet2013) creates a community of users who are using that hashtag phrase.
Right now in Washington D.C. the Supreme Court is discussing the issue of same sex marriage. The Twitter-verse is a buzz with opinions and support for each side of the matter. Users adding #DOMA or #SCOTUS have linked themselves to other users tweeting on the same matter. When a hashtag is used, it automatically hyperlinks the word or phrase to the "trending" list, which is where it matches up with other common tweeters.
Businesses use this tool to connect and track their customers. By promoting the usage of a certain hashtag when tweeting about particular product or service, it connects that community to each other and the business.
Many other social media platforms have adopted the hashtag tool to connect its users. Check out this article on Flickr recently adding the hashtag tool to its iOS app.
http://mashable.com/2013/03/17/flickr-hashtags/