Stickiness is a dimension (daily busy users divided by monthly active users) that indicates whether users keep coming back and value in consumers' lives.
Stickiness in advertising, generally, describes how memorable some thing is--just how well a new or theory "adheres" from the mind of customers.
For mobile programs, it's a metric directly associated with DAU (daily busy consumers) and MAU (monthly active users). Stickiness can be calculated by dividing the daily active users by users that are active. This provides you the portion of your monthly customers that are coming back (the higher, the better).
What arouses people enough to stick around and return? Careful focus on user experience and constantly ensuring that you're supplying value should boost your stickiness with time.