One of the chief advantages of APIs is that they allow the abstraction of functionality between one system and another. An API endpoint decouples the consuming application from the infrastructure that provides a service. As long as the specification for what the service provider is delivering to the endpoint remains unchanged, the alterations to the infrastructure behind the endpoint should not be noticed by the applications that rely on that API.
Therefore, the service provider is given a great deal of flexibility when it comes to how its services are offered. For example, if the infrastructure behind the API involves physical servers at a data center, the service provider can easily switch to virtual servers that run in the cloud.
The ability of API-led connectivity to allow systems to change as easily as plugging in a plug to a socket is key to the modern vision of enterprise IT. Gone are the days of messy point-to-point integrations for connecting enterprise solutions which take time and resources to maintain.