So what does an ‘at-will state’ mean anyway?

Q. What does the phrase "at-will state" mean? Is it just to allow unions under the Taft act? I have an employee who was verbally harassed at work and had his job threatened by being told, "I will have you gone by day's end." I asked the N.C. Dept of Labor and they said the only items covered are EEO definitions (race, color and/or violence in the workplace). Are they correct? Very confused.