Those also obviously correspond to the Insert/update/select/delete SQL operations.
So hooking a RESTful interface direct to your db lets JavaScript on the client talk directly to the database via an http server with no business layer in between. It's obviously a nifty workflow for the "JavaScript all the things" developer.
That said, I think restfulness is a bit of a fad tied to the popularity of javascript-everything. But it has created a limited, simple standard for http services, so that's nice.
Postgrest does not adopt this convention. This decision is not arbitrary, however. Postgrest is conceptually a function that computes a REST API for a PostgreSQL database, and tables in a PostgreSQL can (for better or worse) have compound primary keys, which do not map well to a simple URL path. So Postgrest uses a more general URL syntax. The equivalent of the above is: /some_path?id=eq.123.
Postgrest represents some novel thinking about the use of certain HTTP verbs as well. A lot of this is discussed in the Postrest introduction video here: http://postgrest.com/