1. To give interfaces to developers to interact with your system.
2. Making sure those interactions doesn't harm your system.
3. Free marketing - people who use your API to create their services will also market you.
3. Fluid information delivery
4. Increased integration capabilities. I believe every major technological breakthrough reach public once they have interoperability.
I think overall, APIs increase a systems resilience by enabling them to change different parts without breaking the whole and to monitor and ensure the security of interactions.
