The moving average of a security price is its price over the last x days, where x is the period of the moving average.
For example, the 30 day moving average price of a security is the mean of the closing prices over the last thirty days. The 30 day moving average for yesterday is the average of the closing closing prices for the thirty days up to the day before yesterday.
Moving averages have a number of applications in finance. Chartists use moving averages heavily and see significance in events such as prices moving above the moving average, or different moving average lines crossing.
There is little empirical evidence of the predictive power of the moving averages of security prices. Most of the evidence supports quite the opposite conclusion.