A 50-day moving average is simply the average closing price over the last 50 days, recalculated daily. Plotted on a chart, it turns a jagged line into a smooth one.
Investors watch where price sits relative to it. Above the average is generally read as an uptrend, below it as a downtrend.
The 50-day describes the medium term and the 200-day the long term. When a short average crosses a longer one, traders treat it as a change of mood — nothing about the business has changed.