The thick yellow line is vinyl tubing (with an internal cord) and it connects the gun to the float. So if the fish is too big to drag to the surface (as you ascend from the breathhold dive) then you can let go of the line and allow the fish to be "fighting" the float which has about 35 lbs of buoyancy.
Often you let the line slide through your hand as you ascend and try to keep some tension on the line and limit the depth of the fish, but this makes the ascent harder, so you have to pull only hard enough so that you don't pass out on the way up. It is one of the things that makes the sport exciting and challenging.
Then when you get to the surface, you grab the line and pull. The yellow floatline is 100 feet long and the gun has another 24 feet or so of line and shaft.
Once on the surface, I was pulling in slack, but not making much progress because I was kicking up with probably 25-35 lbs of force, trying to not get pulled under too far and trying to catch my breath after a 60-70 ft dive. You can hear the snorkel bubble when I get puled under a few times. I was nearly completely gassed out, working at 100% aerobic capacity and then my son came and used a "clutch" which is a one-way slider sort of thing that ratchets the line in on the float, which means the diver does not get sucked under (unless the whole float goes too). .
I should have just used the clutch device from the start, but I thought I could probably get the fish up without it (I was wrong).
By that time, the fish was still pulling nearly the entire float underwater. I got about 60 seconds to recover/rest and then I saw the sharks and did another 100% burst of effort to try to haul the somewhat tired fish up and away from the sharks...
That didn't work so well. The wide angle GoPro makes things look further away than they are.
The line does make a mess on the surface. If a shark should grab the fish and dive and you get wrapped in the floating line, you could die. The reason we use the vinyl tubing floatline is because it is low drag but is relatively stiff and tends not to form knots and loops too easily, but the general idea is to try to swim laterally on the surface, pulling in line and leaving it behind you in straight line. When you are fighting with 100% effort to remain on the surface and get air, you can't really do anything else but kick straight up.
