According to Nielsens blog, Twitter had the largest growth rate of the top social network sites in 2008.
To be fair to the others on the list, Nielsen did mark both Twitter and Ning with an asterik stating that these two sites do not meet the minimum sample size standards which means their measures of these two can fluctuate greatly month to month.
Top Growth Social Networks
Other growth social network sites were Tagged, Ning, LinkedIn, Last.fm, Facebook and others. It is interesting that Twitter is considered a social network. I am not sure what their definition of a social network is, but I am guessing since you can follow others it meets their criteria, as opposed to a micro-blog.
Official Nielsen Release
Their official press release can be found here (it is a pdf file). Their blog is a great read also.
Give Twitter a Try
To understand how Twitter works, and why it is so powerful, give it a try. Go to Twitter and sign up for a free account. My suggestion is you use the web interface until you understand how it works, the replies, the direct messages, following etc. You can follow me to test by going here @longest and clicking the follow button.
Twitter Applications and Tools
Once you get the hang of it you may want to use twitter on your mobile phone, add an application to your desktop such as Tweetdeck. Here is my list of the top twitter tools.