Grading on a curve requires first determining what percentage of students should receive each letter grade on a test or assignment and then assigning those grades in order of performance. The top students receive A's until those are exhausted, the next group receive B's, and so on.
Curve grading attempts to arrange student performance across a bell curve. This theory argues that there are relatively few A and B grades and similarly few D's and F's. The vast majority of the students fall into the middle ground and receive C's. It has the effect of forcing the students to compete against one another for a limited number of high grade spots, encouraging students to work hard even if they think they know the material well. It can also excessively penalize those students at the bottom end of the curve, giving them grades below what they might have received otherwise.
Another method of curve grading is to bump the highest student's score to 100 and then add that same amount to everyone else's score. This results in a general upward shift of scores, and can help a class out if a particular test or assignment was too difficult or poorly understood. Teachers can also identify questions that were missed by a majority of the students and add those points to everyone's grade, removing the negative effect of poorly understood concepts.