The process of an in-app purchase (IAP) usually involves pressing a button inside the app, which brings up a dialog from Google Play (or other app market) to confirm the purchase through your account with that app market. An in-app purchase might be:
- a one-off thing to enable a feature forever;
- a subscription, enabling a feature for a limited time;
- a consumable purchase, for a one-time download or a consumable in-game item such as an extra life.
In games, an in-app purchase usually buys you some amount of an in-game currency such as "gems" or "diamonds", and you then spend that on in-game items via some in-game shopping interface. Only the initial purchase (for actual money) is called an "in-app purchase", not the spending of gems within the game.
In utility apps, IAP is replacing the practice of having a free demo and paid "pro" version of an app, or a free app with a "donation key" app, since IAP makes it easier for users to upgrade to the paid version or to donate various amounts to the project.