If you have an ordered series of numbers, then the moving average is a series of averages of chunks of consecutive numbers in that series. An example is probably in order here. Let's say you record the number of cigarettes you smoke each week for a period of 12 weeks and your data is this:
12, 10, 8, 20, 13, 14, 22, 19, 10, 11, 15, 14
If you want to calculate the four-week moving average of this series, you average the first four numbers, then the next four consecutive numbers, then the next four, etc... So you get
12.5, 12.75, 13.75, 17.25, 17, 16.25, 15.5, 13.75, 12.5
The moving average list has fewer numbers than the original list. In a weighted moving average, the numbers have different weights, for example, you might weight the middle numbers more heavily than the ends. In a cumulative moving average, you average more and more numbers each time until the final average which is just the average of the entire set.