Golden Ratio
The Golden Ratio is a mathematical ratio found in nature. The Ancient Greeks believed that this ratio represented beautiful proportions. This ratio is often present in living organisms that grow free from illness or disease. Many artists include Renaissance artists like Leonardo da Vinci used this ratio when planning out compositions, again, because it was seen as useful in creating beautiful arrangements or compostions of forms. The golden ratio is is 1 to 1.618... and is represented by the Greek character phi Φ.
Many arists and photographers still use the golden ratio today as a guide in creating their art. Video on the Golden Ratio.
Rabatment
Rabatment is a simplified version of the golden ratio, where one ignores the exact ratio of 1 to 1.618 and cuts the composition with a square created by the smallest dimension. This line that is created is seen as an important compositional guide.
The concept of rabatment can be applied to rectangles of any proportion. For rectangles with a 3:2 ratio, it happens that the rabatment lines are exactly matched to the rule of thirds lines. In essence rabatment and rule of thirds (see below) are both approximations of the division created by the golden ratio for rectangles that are not in the golden ratio. 
Rule of Thirds
You may have seen a grid with lines like these on your cell phone camera or on a digital camera. These lines are 1/3 from each side and 1/3 from the top and bottom. These lines approximate the line created by using the golden ratio. They are a short hand for the ratio similar to using rabatment.
Placing the horizon at a horizontal 1/3 line is often seen as pleasing compositionally. You will also seen some dots where the lines intersect. Placing important pictorial elements at these intersections often results in a pleasing composition.
