Hashtags are a word or group of words used as a topic on certain social media platforms. They are preceded with a hash symbol – #.
Their primary purpose to to create a tag that is searchable on social media, therefore you will gain, potentially, more exposure. If a particular hashtag becomes popular, for a period of time, it may be seen by hundreds if not thousands. A few years ago they started gaining popularity with Twitter and currently are also common on Instagram, Pinterest, Facebook, LinkedIn and very recently on platforms like Periscope, Musical.ly & SnapChat.
There is unspoken etiquette around the use of hashtags so as a user you are seen not be abusing them or showing you like to spam often. Each platform have their guides of use and up to3 hashtags per posts is rather common.
Hashtags are useful as they can be searched for a period of time they are popular or if they are evergreen. For example, #twitter will be often used as an evergreen tweet, where #superbowl2016 would cease its use after the end of the Super Bowl in 2016.