The movement began about 15 years ago when Yale grad student Jason Sorens wrote a paper discussing the idea of encouraging lots of libertarians to move to one state, in order to try to create a sort of libertarian model, which could inspire others. I.e., the goal was to show that libertarianism was feasible, and even desirable.
It was decided that they would aim to get pledges from 20,000 people to move to New Hampshire. Those who pledged would agree to move within 5 years after the 20,000 pledge total was reached. At the meeting I attended they announced that they had just achieved that pledge target.
Of course they are aware that not all 20,000 will actually move, and thus are continuing to accept pledges. The new goal is to get 20,000 people to actually move.