What is the difference between an "exempt" and "non-exempt" employee?

Ian,
At it's most simple the difference is that "exempt" employees are not eligible (or employers are not required)to be paid overtime compensation at 1.5 times their regular rate for over 40 hours worked in one week.
There are multiple catagories of exemption including the administrative, executive, professional, and sales categories. Each one has defining criteria specified under the Fair Labor Standards Act. Like "independent contractor" status these categories are defined by the government and should be reviewed befre automatically assuming an employee is exempt or nonexempt.
Sometimes employers mix up "salaried" and exempt. An employee can be paid a salary rather than hourly and still be eligible for overtime compensation.
You also have to be careful with exempt employees in treating them as nonexempt in practices like "docking" them for being late and similar practices. You may temporarily "disqualify" them from exempt status.
Don't just take the category titles at face value either- there are descriptions of the activities and duties that represent each category of exemption- the employer doesn't just get to categorically decide.
The penalties if you mis-classify can be pretty starchy...