No one really knows what triggers it, but congestion can contribute to swarming (I don't have any congestion). It could be an early spring, a great honey flow, etc.

When the swarming instinct is triggered, the bees feed worker eggs differently, which makes them into new queen cells instead of into workers. When the new queen cells are about to hatch, the old queen leaves with part of the colony. (This second swarm is a second queen - there wasn't an old queen because she left with a swarm two weeks ago.) The queen flies off. When it starts there are 5,000 to 25,000 bees in a tornado like shape, circling in the first act of swarming. The queen typically lands on a branch or something within 50 feet of the hive (in this case, my neighbors apple tree). When the queen lands, the worker bees that left with her follow her scent and make a bee ball (which you can see in the 1st video). At that point, the new colony sends out scouts to look for a new home (a hollow tree, a space behind the walls of a house, under a patio, etc. When the scouts find the new place, they come back to the bee ball, communicate, and then the bees "swarm" again to fly to their new home. They begin building comb at the new place.

The old colony with a different queen, or a soon to be hatched queen stays in the original place and continues on. Two colonies from one.

One other thing - when honey bees are swarming, they are pretty much harmless. There is no colony to defend. Normally they are very gentle even when you open up the hives. It doesn't show it on the video, but before I popped them into the cardboard box, I crawled up on the ladder and inspected them within a couple of feet with no protection.