What are the differences between the Glossy > Direct and Glossy > Indirect passes in Cycles?
As you might know, Cycles is a Path Tracer, which calculates light "rays" shooting out of the camera, bouncing around, and then finding a light source. This, however, is the opposite of reality, where a light shoots out photons, which bounce around and make their way to our eyes.
A Glossy Direct pass produces a black and white result (a fac, or factor) that shows exactly what part of a scene is made up of visible Glossy BSDF materials.
In the following scene, there is a plane with a Glossy BSDF shader that is reflecting a blue-hued Diffuse BSDF shaded cube. It renders like this:
The Glossy Direct pass shows this:
Note how it excludes the background, the part of the plane hidden by the cube, and even the reflection of the cube. What it shows is only the rays that hit the Glossy BSDF and go directly to a light source.
Not these rays:
Or these rays:
Or even these rays:
A Glossy Indirect pass produces an in color result; at least partially. It is black everywhere except for any reflections.
In the same scene as above, the Glossy Indirect pass renders like this:
Note how it shows only the reflection of the blue cube. This can be especially helpful, because it can first be turned into an alpha mask pretty easily (see the Matte > Color Key node), which allows for compositing on reflections. See how it is used in gandalf3's answer on Post-processing Lightsabers in Blender. It can also be used just by itself. You can edit out the floor of a scene and leave yourself with just an object and it's reflection, which can produce a very cool result:
Above result composited like this:
These are just a few of the possibilities.
For the technical side of things, a Glossy Indirect pass shows these rays, which bounce off the glossy, hit any obstructions, bounce back to the glossy, and then find a light source. They indirectly touch glossy and find light:
Hope this helped and happy Blending!