A language extension is simply anything that goes beyond what the language specification calls for. Your compiler might add new features, like special "min" and "max" operators. Your compiler might define the behavior of division by zero, which is otherwise undefined, according to the standard. It might provide additional parameters for your main
function. It might be the incorporation of another language's features, such as allowing C-style variable-sized arrays in C++. It might be a facility for specifying a function's calling convention.
Using a language extension usually makes your code non-portable because when you take your code to another OS, compiler, or even compiler version, the extension may not be available anymore, or its behavior may be different from what you had originally used.