I like to think about mobile app metrics as a royal family: Retention is King, Conversion is Queen, and Virality is the Princess. Extending this metaphor, LCV (lifetime customer value) is the brooding, well-intentioned-but-misunderstood Lancelot-type knight: he's absolutely integral to the success of the kingdom, but he's completely inscrutable and enigmatic, and he's often at odds with the King. Mobile game retention rates, to a greater extent than any other metrics, are the bellwethers of success.
Mobile game retention rates are the most important metrics to track because they essentially tell you if your game / app / service is any good. Engagement metrics are important, too (average session length; average sessions per day; etc.), but retention gives you the best high-level understanding of how your app fits into your users' lives. There's an excellent post on Games Saved My Life about mobile game retention rates which defines a "successful" retention profile as 40-20-10 (40% day one; 20% day 7; 10% day 30).
Day-one retention is heavily influenced by the quality of an app's user source and the extent to which those users have been targeted: 40% is probably a good number for a casual social game for which users are targeted broadly; a niche app for which users are targeted deliberately could experience higher day-one retention. But from my experience, retention profiles follow (about) the same pattern as 40-20-10 (i.e. 50% decline from day 1 to day 7, 50% decline from day 7 to day 30). So a very well-retaining game might experience a 50-25-12 retention profile vs. a 30-15-7 profile for a poorly-retaining game. Mobile game retention rates vary wildly depending on game niche and market; for most apps, the "objectively good" retention profile of 40-20-10 is a reasonable goal.
Considered from a different angle, your retention profile gives you a rough estimate of the lifetime of your average player (i.e. for how long they'll play -- in calendar days, not in game-play days). Knowing this gives you one half of the LCV equation; if you know your daily ARPU value (important that this is also calculated in calendar days and not game-play days), then you can value the average user.
The way I architect an analytics system to capture retention is to retrospectively indicate -- from days 1 through 7 and then 14, 30, and 365 -- on which day a user played. There are two ways to go about doing this: by keeping a record of each user in a "users" table, with columns apportioned for each retention day, or by keeping a record (similarly constructed with retention columns) for each user for every day he plays. The second approach obviously requires more data to be stored (a record per user per day), but it also allows you to track retention relative to any point in time (not just the user's registration). This allows retention changes to be tracked after major feature updates or product launches easily. For example, if a product was launched on January 1st, and a record is stored for each user on each day they play, then summing up the day 1 retention column on January 2nd and dividing it by a count of records on January 1st gives you day-1 retention for the product launch.
As the King of all Metrics, retention rate provides a product manager with the best appraisal of her app's fundamental viability -- it's the essence of whether an app is good or bad. But retention also gives a product manager a reasonable estimate of how long her users will remain with the app, which is the foundation of calculating lifetime value.