Most people want followers when they first sign-up for Twitter. One way to do this is by using a service that promises "thousands of followers". Unfortunately people don't always read the fine print, so they don't realize they've entered into a "devil's bargain" .
They get more followers, but they've also agreed to allow the "service" to send spam tweets to their followers in their name. In some cases these spam tweets are sent once an hour and they go on forever.
You can look for an opt-out option on their website (the URL is included in the spam tweets) but the opt-out doesn't always work. In addition, sometimes their url "shortener" (e.g. tinyurl.com) figures out they are spamming and drops the target URL. In that case you may not be able to figure out what the actual URL is for the "service".
One sure-fire way to stop spamming your followers is to change your twitter password. Then the "service" can no longer access your account to send tweets.