An ORM is a library integrated into a language runtime. Postgrest is a service – a separate process – which sits in front of a Postgres database, offering a RESTful HTTP API over that database. This means web or mobile HTTP clients can access the database in a safe, controlled manner.
Postgrest basically shifts the work of writing a basic CRUD API (a task for which you would probably use an ORM) to declaring a SQL schema. From that schema, it infers which endpoints should exist and what they should do. For a certain class of web app, this can be a HUGE time saver.
I'm designing a web app that doesn't need much actual backend, save some static data slightly too large to ship with the static files. I have nginx serving static files and proxying db requests to postgrest.
Postgrest basically shifts the work of writing a basic CRUD API (a task for which you would probably use an ORM) to declaring a SQL schema. From that schema, it infers which endpoints should exist and what they should do. For a certain class of web app, this can be a HUGE time saver.
Beyond that, consider checking out the "Motivation" section of the website: https://postgrest.com/en/v0.4/intro.html