The main objective of API is for two applications can communicate with each other. API allows external agents to communicate with our application.
The main purpose of API is interoperability.
In Simple way: Methods of communication between software components. Example - Authentication with Facebook/Google.
API which is developed to access web applications by using HTTP protocols is called web API/Services.
REST stands for Representational state transfer. REST is an architectural style. It defines several rules/guidelines to develop Web APIs/Web Services.
The API which is developed by using REST Architecture is called RESTFul API.
REST is basically an architecture where a RESTful API is an API that implements REST.
Django rest framework provides several toolkits to develop RESTful API very easily. This framework internally uses all Django facilities like models, views, templates, ORM etc.