Working at the walk you should have gotten a feel for being able to get your horse working IN the bridle and ON the bit. Some of you may still be asking "What does that mean?"
When the horse is In the bridle, they are working with their head in a position that allows them to use it to balance and typically they are working on the vertical, meaning that if there were a line or a wall in front of them, their forehead down to their nose would be flat up against it. Sometimes their head will be lowered and other times it may be carried a bit higher, but they should be breaking over at the poll which should be relatively level with or just slightly higher than their withers. I will use the photo of Kat again here to illustrate this. He is on the vertical and his poll is slightly higher than his withers.
When the horse is On the bit, they are literally on the bit. They aren't sucked back behind it, which is typically a reaction of having too much bit and they aren't gaping at the mouth, sticking their nose in the air, running thru the bit or ignoring it. Being On the bit, when you move your hand to give a cue, the horse will respond instantly. In order for the horse to be on the bit, they have to be comfortable with the bit. It has been chosen for this horse based on their level of training and what you will be trying to accomplish. The bit will also be adjusted properly to fit this particular horse, they readily accept it and are confident and submissive to your hands, not trying to escape, evade or run away from it. This means you have shown them that they can trust you not to hang onto them with a death grip or yank and jerk them around.
Another way you can look at the In and On ideas is this- In the bridle is the up and down movement of the horses head and neck. On the bit is the lateral or side to side movement of the head and bending of the neck. With both Up, Down and side to side movement all going on at once, it can be easy for things to get out of control quickly. This is where small movements come into play and can make big changes. If you can instill the confidence in them from the begining that contact is not a bad thing, it is much, much easier to pick them up and guide them along, rather than dealing with a horse who has been 'beat up' in the face and has a learned fear reaction. You have to trust your horse so they can trust you.