You have two options to handle alpha values (not counting shaders), alpha testing and blending. The first two rows of the code you posted is to enable blending, and the last row is to set the threshold for alpha testing.
Either enable blending, for example:
glEnable(GL_BLEND);
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
Or enable alpha testing, for example:
glEnable(GL_ALPHA_TEST);
glAlphaFunc(GL_GREATER, 0.1f);
The main difference between them is that blending can have semi transparency while alpha testing is either true or false. So why use alpha testing when it also can be slower? The most common answer is simplicity, as you can render your objects in any order, while blending requires you to (in most cases) sort all draw calls to draw everything back to front.
Mike