Here's my view...
The attraction to making RESTful services is that rather than creating web-services with dozens of functional methods, we standardize on four methods (Create,Retrieve, Update, Destroy):
REST is becoming popular because it also represents a standardization of messaging formats at the application layer. While HTTP uses the four basic verbs of REST, the common HTTP message format of HTML isn't a contract for building applications.
The best explanation I've heard is a comparison of TCP/IP to RSS.
Ethernet represents a standardization on the physical network. The Internet Protocol (IP) represents a standardization higher up the stack, and has several different flavors (TCP, UDP, etc). The introduction of the "Transmission Control Protocol" (guaranteed packet delivery) defined communication contracts that opened us up to a whole new set of services (FTP, Gopher, Telnet, HTTP) for the application layer.
In the analogy, we've adopted XML as the "Protocol", we are now beginning to standardize message formats. RSS is quickly becoming the basis for many RESTful services. Google's GData API is a RSS/ATOM variant.
The "desktop gadget" is a great realization of this hype: a simple client can consume basic web-content or complex-mashups using a common API and messaging standard.