Twitter users sometimes go crazy to increase their followers and most of the time it results in a huge Loss, If you are receiving lot of Tweets offering you to increase your Followers (see the screenshot)
then simply ignore them, it is the latest Twitter Scam, The Service offers you to increase your followers by thousands in a click and needs your Login info, but it sends tweets about itself and affect all your followers as well, if they also login there.
Some other people are also trying the same method with same domains, so be careful. Twitter is trying to reset password of all infected users and to shutdown the service. Till then be careful and inform your Followers about this.
~ Enjoy Tweeting