The use of a # hashtag (US pound sign) was introduced by Chris Messina in 2007 as a way to group tweet conversations. Little did he know then how much they would go on to be used!
Keywords can be preceded with the #hashtag – e.g. The growth of #socialmedia has been exponential. Using the Twitter search facility the use of such a keyword will bring together all tweets containing it.
Another use is an organised tweet chat. Very often this is a set time for a duration of a hour where people discuss topics and answer questions. e.g. #edchat #edtech #HSUchat. A useful and comprehensive list of educational hashtags can be found here: http://edudemic.com/2011/10/twitter-hashtag-dictionary/.
Another example is using a hashtag to bring together tweets at an event. Many conferences these days will agree a #hashtag prior to the event commencing to enable delegates to tweet prior to, during and after an event. By searching for and saving the agreed hashtag it is then possible to follow within one stream the tweets from that event.