Variations are a way to relate two variables. For example, if we have the equation A=LxW we can say that Area (A) varies directly with Length (L). It also varies directly with width (W). A direct variation means that the variable on one side is on the "top" of the fraction.
An inverse variation can be seen by the equation, a=v/t. Therefore, we can say that the acceleration(a) varies inversely with time (t). An inverse variation means that the variable on one side is on the bottom of the fraction, underneath. (In the previous example, "a" also varies directly with "v".)
If I know that the formula for speed = distance/time I can say that speed varies directly with distance.
Hopefully this helps.