QuoteURL is a way to keep tweets grouped together that might not be in a threaded conversation. Also it grabs them before they might get washed away but the tide of tweets over time.
To grab a tweet you must get the individual status URL from the web itself and paste it into the site. If you wish not to log in, you can grab up to 4 tweets. If you decide to log in you can get up to 10. This helps control the API limits that might be encountered once this site gets a lot of traffic.
What I did like was the ability to aplit the screen to get to the Twitter homepage or search and drag tweets right over into QuoteURL to add in! Very slick. A new page and URL is then created with all the tweets you captured and you can have it for later referral.