Executive Summary

SWIG is an interface compiler that connects programs written in C, C++, and Objective-C with scripting languages including Perl, Python, and Tcl/Tk. It works by taking the declarations commonly found in C/C++ header files and using them to generate the glue code (wrappers) that scripting languages need to access the underlying C/C++ code.

John Ousterhout has written a paper that describes the benefits of scripting languages. SWIG makes it fairly easy to connect scripting languages with C/C++ code.

You might use SWIG in a number of ways:

Building more powerful C/C++ programs. Using SWIG, you can replace the main() function of a C program with a scripting interpreter from which you can control your application. This adds quite a lot of flexibility and makes it easier to build extensible programs. When combined with Tk, you can also build graphical user interfaces.
Rapid prototyping and debugging. SWIG allows C/C++ programs to be placed in a scripting environment that can be used for testing and debugging. For example, you might test a library with a collection of scripts or use the scripting interpreter as an interactive debugger. Since SWIG requires no modifications to the underlying C code, it can be used even if the final product does not rely upon scripting.
Systems integration. Scripting languages work fairly well for controlling and gluing software components together. With SWIG, different C/C++ programs can be turned into scripting language extension modules. These modules can then be combined together to create new and interesting applications.
Construction of scripting language extension modules. SWIG can be used to turn common C/C++ libraries into components for use in popular scripting languages. However, before doing this, you might want to do a search to see if someone else has already made such a module.

SWIG is sometimes compared to interface definition language (IDL) compilers such as those you would find with systems such as CORBA and COM. Although there are a few similarities, the whole point of SWIG is to make it so you don't have to screw around with that stuff. If anything, it's much more of a rapid application development and prototyping tool. Specifically:

ANSI C/C++ syntax. SWIG parses a form of ANSI C syntax that has been extended with a number of special directives. As a result, interfaces are usually built by grabbing a header file and tweaking it a little bit.
SWIG is not a stub generator. SWIG produces code that you simply compile and run. You don't have to fill in any stubs or write special code as you do with RPC-like systems.
SWIG does not define a protocol nor is it a component framework. SWIG does not define mechanisms or enforce rules regarding the way in which software components are supposed to interact with each other. All it does is provide the glue needed to hook C code to other languages.
Designed to work with existing C/C++ code. SWIG requires little, if any, modifications to existing code. For the most part, it encourages you to keep a clean separation between C/C++ and its scripting interface.
Extensibility. SWIG provides a variety of customization options that allow you to blow your whole leg off. SWIG does not enforce any rules related to programming morality.

A number of papers and tutorials describing SWIG are available. You can also view a simple tutorial to see an example of SWIG in action, or check out how other people are using SWIG in their projects.

SWIG has been freely available in various forms since February, 1996 and a large number of developers have made contributions. Today, SWIG remains an all-volunteer effort. Approximately 560 people subscribe to the SWIG mailing list (swig@cs.uchicago.edu) and a public CVS repository is available at the University of Chicago.