Moving Average is a statistical term used to show the average value of something over a changing period of time. This is frequently used in technical analysis by comparing different moving averages (20 day, 50 day, 200 day etc) to see long term and short-term trends.
The calculation for a moving average is simply the average of a period of time (i.e. 20 days) moving forward over different periods of time.
Moving averages are used along with MACD analysis to predict trends and momentum, for example when a short term moving average rises above a long term moving average, this is taken as indication of an upward trend.