Hash tags are used to tag your tweet with something.You can use this to mark it so when someone searches by that hash tag they can see everything people have tweeted that was tagged with that. For example you could tweet "I am tired of all the rain #Mondays" Then you can click on the #Mondays and see all tweets with that on it.
A hash tag can represent many things throughout expression of emotion and action. Hash tags are often used to relate to people with a similar, or exact hash tag. A trending topic on Twitter.com is a hash tag that has become relevant throughout the constant tweeting of the hash tag.