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If your app offers subscriptions, in-app purchases (virtual goods/services, content or in-app functionality/upgrades) or facilitates any kind of e-commerce transactions, there must be a way to accept payment from users. IAP is by far the simplest option, since payments are handled by Apple, Google, Microsoft, etc. as part of their app store ecosystems, taking a 30% cut in the process (20% for Windows Phone).
For e-commerce apps selling real-world goods or services (anything outside of the app itself), the onus is on the publisher to process user payments from credit/debit cards, PayPal, bitcoin, Boleto or whatever payment methods are most popular with their users. Payment processing is a complex business, but many 3rd party services exist that can be integrated to facilitate payment processing, billing, etc.