The MACD is possibly one of the most well known Technical Indicators. The acronym means Moving Average Convergence Divergence and the indicator is calculated as the difference between a shorter and a longer moving averages.
Moving averages are used to gauge trends. The basic assumption is that a moving average helps identify a trend, and therefore when a short-term one diverges or converges to a longer term moving average, the trend is meant to continue or invert. Generally, when one moving average crosses the other traders assume the trend will invert.
MACDs are defined by the windows of the two moving averages, for example one can have 1 month vs. 3 months, 12 weeks vs. 24 weeks, and so on.
Possibly the most well known MACD combo is the 50 days vs. 200 days one, which gives rise to two colorfully named inversion events: the Golden Cross and the Death Cross. These are, respectively, the occurrence of the 50D average crossing above the 200D one, and the mirror event when the shorter average crosses below.