It's called a static library.
Effectively it's a library of code. It usually exposes a number of functions, which can be called if you link the .a with your program.
In C and C++, you'll need an .h file to do that, in FB you'll need a .bi file, etc.
On Windows, .a files are normally Win32 .lib files that have been renamed to work with Linux tools that have been ported to Windows, like DevC and FBIDE.
Jim