Updated at 8:23 PM with statement from TwitterHawk creator. See end of post.
The service actually looks for more than just words. It can also scan for posts from specific locations (how it determines location is not clear to me) or for tweets that are calculated to have generally positive or negative sentiment, or for those that have links embedded in them.
The examples given on the site are for marketing: If you have a coffee shop, for example, you can use TwitterHawk to monitor for tweets about "coffee" in your city, and then send them an automatic reply. If I Twittered, "I could really go for a cup of coffee," for example, I might get a reply back via the service from a coffee shop owner saying "@Rafe, Come to Joe's Coffee and try our Blogger's Blend."
TwitterHawk has rate limits in place to prevent it from becoming a horrible spammer and abuser of Twitter resources. But it's still a highly commercial concept and will clearly set a few people on edge. It's available at no cost for now, but if ever there was a Twitter service that deserved to have a fee attached to it, this is it.
I set up a test TwitterHawk account that monitors Twitter for one word: "Bananastan." Post an item with that word in it and you may see an auto reply sent to you from the @Webware account.
Update: TwitterHawk creator Chris Duell appears sensitive to the spam issue, and has updated the service so it can only send out one message a day per monitored term. When I tested it earlier, it could send one message per hour. He has posted a press release entitled "TwitterHawk and Spam." Key statements include, "We do not in any way condone using TwitterHawk to aggressive SPAM based marketing tactics to harass or annoy people with advertising material on a regular basis... Our number one focus right now is ensuring that Twitterhawk adds value to all those who come in contact with the service... More SPAM protection measures will be being put in place in the comings days."