This is a Carolina Rig, which is a common system used in the NYC area when anchoring the dive boat to a wreck or other dive site.
The anchor line runs from the bow of the dive boat to a strong attachment point on the bottom. In some cases (rarely seen in our area) it may run to a permanent mooring site that is nearby but separate, to minimize damage to the wreck. There are two short downlines hung from the dive boat at the stern and midship with weights to keep them stable and vertical. A horizontal "granny" line runs from the stern downline to the midship downline - fixed at a depth of around 15 feet. It then continues forward to the anchor line, where it is attached to a weighted ring which can slide up and down, minimizing the jerking on the line that can happen in heavy seas. There is also a trail line, which floats on the surface behind the boat. Since the boat will be normally floating downcurrent from the anchor line, this mean that any divers who lose contact with the boat or the other rigging may be able to grab the trail line to keep from drifting away.
This system has a number of advantages. Since divers generally enter and exit the water from the stern of the boat but need to descend on a line from the bow (often upcurrent), it gives dive teams a secure place in shallow water to quickly get below the waves, and to sort out any problems before descending to the wreck. It can be challenging to deal with issues on the surface, especially in heavy seas, and a surface swim against the current from the stern to the bow anchor line can be exhausting. Moving slowly, and pulling hand over hand along the granny line is much easier.
The length of the granny line means that multiple divers can use it as a reference to maintain this depth and spread out, either for pre-descent checks or for safety stops (and decompression stops). This is much better than having a number of divers bunched up on a single anchor line around 15 feet. One important precaution, however, is that it is very important to have good buoyancy control. If one diver is significantly positive or negative and they are hanging on to it, they will pull the whole granny line (and all the other divers) up or down.
Once any stops have been completed, divers simply move aft to the stern downline and ascend, which will place them just off the ladder. If a number of divers are boarding around the same time, it's a simple matter for them to grab the trail line, spreading out to a safe distance but not drifting off, while each diver reboards the dive boat in turn.
Unlike the tropics, most local dive boats have fins-on ladders with big steps, and the crew does not want you to remove your fins in the water. This prevents a diver from accidentally losing contact with the dive boat and drifting away with no fins for propulsion.