There are many different Key Performance Indicators (KPI) used in online games to determine the success of a game. One of the most basic, most common and most important metrics is the retention rate.
Retention rate measures the amount of players who join a game and return to continue playing after a predefined time period.
Most common is the use of three different time frames, the 1-day retention rate, the 7-day retention rate and the 28-day retention rate (some use 30 days but because 28 days is exactly 4 weeks later and some players tend to play always on the same weekdays, 28 days is probably the better metric). Usually the retention rate is given as a percentage of returning players.
A successful facebook game for example should have retention rates somewhere near 40-20-10, which means 40% of the players return on the next day to continue playing, 20% should return after 7 days and 10% after 28 days.
Sadly retention rate is often calculated in different ways and even many commercially offered metrics tools either don't feature this very important indicator at all, or use very different ways to calculate it.