Hashtags are a quick and dirty way to create labels so that information is easier to find, and events easier to follow. Think of them both as user-defined slugs but also, because of the nature of twitter, as informal ad hoc groupings of people. Conferences or events will often try to agree on what hashtags to use beforehand, so that everyone can follow what is being discussed without having to know all the individual twitterers covering that event.
Hashtags could be countries (#indonesia), people (#obama), events (#worldcup), topics (#socialmedia), or spontaneous shared opinions/experiences (#whatididlastnight)
Add a hashtag
Simply put a # before the word (without any space) somewhere in your tweet (usually at the end). Check out what other hashtags are being used first.
Searching via hashtag
You can search hashtags via Twitter’s own search engine. More here.
Or on Tweetdeck. More here.
Or via third party services. Like these:
#hashtags.org is good for seeing what people are talking about, and whether the issue is still hot:
What the Hashtag?! is similar, but perhaps with more information, including user-contributed definitions of what the hashtags mean.
When things are really buzzing it’s worth following a hashtag on Twitterfall: a cascade of tweets drop down the page:
[...] Twitter: Hashtags [...]