Unless you've never been on the internet (impossible if you are reading this), you have probably seen the symbol # popping up in messages and in posts online.
It used to be used to show a number, and was often known as the number sign, or hash. In North America it was also known as the pound sign, but not any more. The internet has changed all that.
Today you are just as likely to see it in front of a #word or #phrase as a number, and this is when it's called a hashtag, a word combination of hash and tag. It is a genuine word, and was added to the OED in 2010, you can even use it in Scrabble.
But what is a hashtag used for? In social media, especially on Twitter, the hashtag is used to identify messages on a specific topic. Twitter identifies trending topics by the number of times a particluar hashtag is used, and by using # you can set the theme for a post or message, or you can use it to search for a topic of interest.
However, hashtags can get pretty weird: Hashtags have to be written as a single word, without any spaces, so you can't hashtag a sentence, you have to combine the words together. That's why you get "trending" topics such as: #Brangelina (the Brad Pitt and Angelina Jolie meltdown), the more positive #socialgood, #alllivesmatter, and the strange #ff (which I am assured means Follow Friday).
If you go to https://www.hashtags.org/ you can see some of the most recent trending hashtags, and how often a particular hashtag has been used.
If you have a Facebook, Twitter, G+ account, you should give hashtags a go. If you want to know how (and how not to) use them, Hootsuite have written an informative article. https://blog.hootsuite.com/how-to-use-hashtags/