An RPC framework in general is a set of tools that enable the programmer to call a piece of code in a remote process, be it on a different machine or just another process on the same machine.
In the particular case of Apache Thrift, we talk about a framework designed to be efficient, and available across both OS platforms and programming languages. Additionally, you have some flexibility regarding transports (such as sockets, pipes, etc) and protocols (binary, JSON, even compressed), plus some more options like SSL or SASL support.
For example, you may set up a server on a Linux machine, written in C++ which offers some service to the world through a JSON-based protocol over HTTP. This service may be called by a client program written in Python, running on a Windows machine. The code for both server and client is generated from a Thrift IDL file. To get it running, you basically have to add only the intended program logic and put all the pieces together.
The single best reference for Apache Thrift is still the Apache Thrift Whitepaper. Although slightly outdated in some of the details, the underling concepts are still valid. Another good read is Diwaker Gupta's "Missing Guide", and last not least the forthcoming book from Randy Abernethy.
For beginners, I would recommend to start with the Apache Thrift tutorial suite, these examples show a lot of the core features. If you run into questions, you are welcome to ask here on SO, or on the Thrift mailing lists.
