REST is an API architecture pattern; REST APIs are distinguished from other APIs by their design. They offer a standardized interface for interacting with data resources. A REST API for a financial institution would be structured similarly to one for a hospital system; different problem spaces, but similar API design.
Any REST or non-REST API can be used by multiple applications, so it’s not safe to say that REST APIs are more reusable than non-REST APIs. REST is simply a common standard for implementing data access/manipulation operations through an API.
For example, if I had a web API that managed
foo objects, I might have the following HTTP endpoints for a RESTful API:
GET /foo/<id> # Look up a foo POST /foo # Create a new foo
Or, if not following REST guidelines, I may have:
GET /foo?id=<id> # Look up a foo POST /newFoo # Create a new foo
The latter API is technically just as reusable as the former, but the former is more standardized and will be more recognizable by developers who have used REST before.
To learn more about the standards/guidelines of REST, see Representational State Transfer.