Calculation :
The blue line of the MACD is obtained by substracting the y days exponential moving average from the x days exponential moving average
The red line of the MACD is obtained by calculating a z days exponential moving average of the blue line.
x, y and z are the MACD parameters, typically equal respectively to 12, 26 and 9.
The MACD histogram is obtained by substracting the red line from the blue line.

Interpretation :

MACD is an excellent trend indicator, and partly minimises the delays obtained with the usage of simple moving averages.
There are 2 basic ways to use MACD:
Crossings:
A buy opportunity appears when MACD crosses upwards its signal line.
A sell signal may be triggered when MACD crosses downwards its signal line.
The divergences between the MACD histogram and the price quote identify major reversal points and give strong buy/sell signals.
A bullish divergence occurs when stock prices make new lows while the MACD histogram fails to make new lows.
A bearish divergence occurs when the stock price makes new highs while the MACD histogram fails to make new highs.
The bullish and bearish divergences are more significant when the MACD is in an overbought or oversold level.
The opportunities appearing in longer time horizons (weekly, monthly..) generate larger price movements.