Difficult to explain without doing proper diagrams - you might be able to work it out just by playing around with the settings yourself. Anyway, in basic terms a single vertex (dot) can be connected to multiple bones. It can be connected at a total of 100% connected. This could be one bone at 100%, or 2 at 50% each and so on. It doesn't have to be 50%/50%, it could be 10% and 90% (or any other number).
This isn't the best example, but it was the quickest one I could think of, and involves a hat (which you've already done) :
A hat is simpleEvery vertex of the hat is connected to the head bone, at 100%. If the head moves forwards, the hat maintains its relative position exactly. If the head turns left or right, the hat will turn left or right as well. Any movement applied to the head is applied to every vertex on the hat. No other bones influence it.
A hoodNow imagine a hood. The hood covers the whole head, and a section of it rests upon the shoulders and neck. If we attach the whole model to the head, then when the head turns, the shoulder and neck sections will "cut through" the model. If the lower sections were only attached to the neck, then the top half would stick to the head and the bottom half would stick to the neck - so when the head turned, the model would sort of twist strangely, and probably have a load of glitchy polygons sticking out everywhere. Therefore the top half of the model could be 100% connected to the head, and the lower half could be 50% connected to head and 50% connected to the neck. This would mean when the head turned, the lower half would turn
slightly - it would half-follow the movement of the head and half-stay where the neck was. This would mean there was a softer movement in the lower part of the model, so it would twist slightly, but seem much more natural. You may find further that parts of the model should move when the shoulders move, so you may want to connect part of the model at 33% head, 33% neck and 33% nearest shoulder.
Here is an awful MSpaint diagram :
Not the best diagram I've ever made.
I can make some clearer diagrams in the "more advanced rigging" tutorial, but it's going to take a little time to create and collect all the proper screenshots and bits and actually write the thing. The main areas you'd need to use the connection strengths would be with any clothing item which crosses a joint (i.e. elbow, shoulder, knee, waist, hip). The easiest way I found to test them was by loading in some extra animations and seeing how it moves (in Fragmotion, this is "merge animation", then select walk, run, use etc).
Here is quite a good example (from this
post) :
See those shoulder bits, and how his arms "cut through"? The shoulder pads are connected only to the spine bone. This works great for walking and so on, but when his arms move like this, it clashes. Some combination of these connections may be needed to make the shoulder pads "move up" when his arms do (i.e. 75% spine bone, 25% arm bone) - but without making them move down too much when his arms are lowered. It's tricky, and so far I haven't solved this myself.
The easiest way is probably to cut the shoulder pads off and have them as separate objects which rotate along with the arms, or to alter the model so they are slightly higher at the front.
Karpov has done a brilliant job with rigging some of the existing models (and the base human, of course) so a good thing to do would be to load up some of those models and study how the weighting is done. Pick the existing armour which is closest to the one you want to rig, and roughly copy the layout. After that, you tweak it until it works.
Hope that gives you enough to get started anyway. Good luck, and ask me if you've any little questions