The mean arterial pressure is the average of all the pressure measured millisecond by millisecond over a period of time. It is not equal to the average of systolic and diastolic pressure because the diastole is about twice as long as systole in normal conditions. Therefore, arterial pressure remains nearer to diastolic pressure than to systolic pressure during the greater part of the cycle.
I like this way of explaining MAP, because it sets up what is, in my opinion, a better equation for MAP (and often simpler):
(1/3 x systolic pressure) + (2/3 x diastolic pressure) = MAP
Try it and you'll see that you get the same result as other equations - and the above equation is easy to remember.