What is REST?
REpresentational State Transfer. It describes how one system can communicate state with another. One example would be the state of a product (its name, description etc) represented as XML, JSON, or plain text. The generalised idea of state is termed a resource.
What position does it occupy in a web architecture ecosystem?
REST is commonly associated with the web services interface since HTTP is by far the most common carrier protocol. In the 7-layer model it exists at the application layer. However, see the next section.
How tightly (or loosely) it is coupled with protocol?
REST is not HTTP. It uses HTTP because in its most general form REST exists to assist a machine in mapping the concept of a verb against an arbitrary collection of nouns. HTTP contains a useful set of generic verbs (GET, PUT, PATCH etc) that can applied to arbitrary nouns expresssed as URIs using HTTP e.g. GET http://example.org/Product(54).
What are the alternatives to REST and how does REST compare with them
This is akin to asking "How RESTful is my approach?" Use the following list (summarised from the Richardson Maturity Model as described by Martin Fowler):
Level 0 - The swamp of POX
Use POST for everything (reads, writes, deletes). This is SOAP, POX, RPI etc. You're just using HTTP as a tunnel for your own protocol. You target a single endpoint that does everything based on the contents of the request body.
Level 1 - Resources
Use POST for everything. Target multiple endpoints designed to serve up information about a particular thing. You've just discovered resources.
Level 2 - HTTP verbs
Use HTTP verbs against resources. Now you're GETing it. POST is to create, PUT is to overwrite, OPTIONS for available operations, DELETE to, well, delete the resource. As a result of the use of these verbs different HTTP status codes start to become more relevant (202 ACCEPTED anyone?).
Level 3 - Hypermedia control (HATEOAS)
At this point you make the final leap and introduce hypermedia as a flow control mechanism. A REST client needs no prior knowledge about how to interact with any particular application or server beyond a generic understanding of hypermedia. This can be communicated in HTTP through the Content-Type header field. Text formats include AtomPub and (more concise) HAL, while HyperAudio works well for audio streams (see SoundCloud et al)