Hashtags originated on Twitter as a way to search for specific topics. If you were tweeting about your favorite band, you would hashtag the band name at the end as a way to categorize your message. The tweet would then come up if someone searched for #thatband.
Facebook has recently adopted the hashtag and all public messages that include # are now searchable.
Where is the hashtag on my keyboard? Just hold down shift and click the number 3 to produce the hashtag.