"apt: Debian package manager." (5 words)
Apart from that, you need an ANSI C++ compiler, but not g++ 2.7.*. Instead, g++ 2.8 or newer egcs compilers should work great. While nobody has tested apt on other compilers, you also require a properly functioning Standard Template Library (STL). Moreover, you need a C library with standard POSIX functions and a BSD socket layer. Most Single Unix Specifications conforming OS should meet these requirements, though.
Finally, refer to the Build-Depends information in debian/control to check for any additional requirements, some of which may be Debian-specific. One thing to note is that C++ global constructors are not linked correctly with non-shared libraries. While this is probably the behavior expected of the linker, a workaround is yet to be designed. A simple fix is to add a reference to debSystem in apt-pkg/init.cc, with assert(&debSystem == 0) sufficing.
Version 0.7.24: N/A