Twitter, Trending Topics, and Hashtags

In Twitter, the hashtag (#) are like tags with which you can emphasize on a certain point in your tweet. It can also be used as a link to group a specific subject into one easy to access area. For example, when I tweet something like "Hey, @google is releasing its own smartphone and it's called #Nexus #One !". Here @google refers to the company Google (since they've have a Twitter account, it's always better to mention their Twitter account than just Google). The hashtags - Nexus and One - emphasize what the tweet is all about. Hopefully you get the idea! Twitter officially didn't support hashtags until about a couple of months ago.
Coming to trending topics, these are the hottest topics of discussion all over Twitter. Say for example, when New Moon was released and everyone started tweeting about it (either as "New Moon" or as "#newmoon) - it became a trending topic.