What is REST and what are its key principles?

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REST (Representational State Transfer) is an architectural style that treats your data as "resources" you address with URLs and act on with HTTP methods.
Instead of inventing a custom protocol, REST reuses the plumbing the web already has: URLs name things, HTTP verbs say what to do with them, and status codes report the outcome. A few principles make an API "RESTful":

Resources identified by URLs - every thing you can act on (a user, an order) has its own address, e.g. /users/123. The URL is a noun; it names what, not how.
HTTP methods define the operation - the verb carries the action: GET reads, POST creates, PUT replaces, DELETE removes. The same URL /users/123 behaves differently depending on the method.
Stateless - the server keeps no memory of previous requests. Each request must carry everything it needs (auth token, parameters), because the next request might land on a completely different server.
Uniform interface - consistent URL patterns and predictable response formats (usually JSON) so a developer can guess how the rest of the API works from one endpoint.

Why statelessness matters: because no request depends on server-side session memory, you can put ten identical servers behind a load balancer and any of them can answer any request. That is what lets REST APIs scale horizontally - it is the property that makes them cheap to grow. The trade-off is that the client must resend its identity (e.g. a bearer token) on every call.
Go deeper:

Wikipedia: REST (Representational State Transfer) — history, the six architectural constraints, and how the term entered common use.
 Fielding dissertation, Ch. 5: Representational State Transfer — the primary source where Roy Fielding first defined REST and derived its constraints.