Being stateless is a crucial characteristic of a REST service. Indeed, HTTP, as a stateless protocol, doesn't keep track of all the information about the connection between the client and the server once the communication ends.  

A stateless protocol forces the client to fulfill the request with all the required information each time it needs some information from the server. Let's take one of the previous URIs:

https://api.nytimes.com/svc/books/v3/lists.json?api-key={your_api_key}&list=hardcover-fiction

The client has to send the API key with each request to be authenticated by the server. Furthermore, it must store the API key information.

Statelessness is very important if we wish to take advantage of REST services. Nowadays, with the rise of highly distributed systems, it is difficult to deal with stateful services because this requires the states to be managed and replicated on different servers. A stateless approach helps delegate state management to the client.