The idea is that your legs are like huge bundles of bamboo stuck in the ground at angles leaning over a river. These bundles then have more and more bundles tied to them at progressively lower angels until the two sides of the bridge meet in the middle. By staggering the bundles you create many triangles in the structure and it becomes a self supporting woven structure, which is both strong and quite flexible.
In other words, he was saying that the two legs are a connected structure which is constantly redistributing the weight of the torso.
Luo Dexiu and the gang over at formosaneijia are using the metaphor to mean the act of crossing over. If you are going to have a fight at a bridge and you meet your opponent in the middle, you both have equally limited space to maneuver. Step back and you are below your opponent, step side and you're in the drink.
However; if your opponent decides to cross the bridge first you can gain an advantage by attacking him just as he is exiting the bridge, at the moment where his maneuverability is limited and yours isn't.
This complex metaphor is used to talk about how we enter a fight and close the gap between us. Speed, power, technique, and the use of timing all change dramatically as the two fighters get closer and closer together. (Basically we move through this approximate progression in an instant: Kicks, jabs, stomping, slaps, hooks, throws, knees, elbows, shoulders, more throws, grappling.)
Thus the bridge is often the movement or technique one uses to get in closer. If you "cross the bridge first" your technique should compensate for that moment of vulnerability just as you "get off the bridge." For instance, someone will often step in fast faking with the back of their hand outstretch, if this is met by the opponent's hand, one can can sense the opponents intentions, direction, and power at the moment of contact and spontaneously use that information to inform the next part of their attack.
Others, like the Blacktaoist, are, by extension, using the term bridge to mean one's arm. If the arm is the first contact with the opponent then it needs to have extraordinarily good structure, so that it can take all the heavy traffic that is going to be traveling over it!Â More traffic, more power.Â If you have a weak bridge (that can't handle much traffic), it doesn't matter how good your techniques are, your opponent's bridge will send more heavy traffic (o.k. how about troops then?) to dominate your side of the the bridge.