[by the time I finished my reply Bob provided a much more concise summary - read this if you have spare time
]
The bobbin rest is very useful if you are doing (for lack of better term) multi-level tying operations. What the heck does that mean?
Let's start with a wolly bugger. Everyone ties 'em sooner or later. It has a palmered hackle over chenille. On a stationary vise, both are wound around and around the hook shaft. The results can be (but not always) uneven and it's not easy to re-wrap to straighten, especially because you want the stem to be against the chenille with the barbs pointing outward with no twisting of the hackle. Wrapping the hand around the hook inherently twists the feather. That's why people make and buy expensive universal hackle pliers that hinge at the union of handle and jaws... to provide the degree of freedom to keep a feather straight during the winding process.
With rotary, you hold the feather in the desired position and turn the fly. It can't twist unless you go out of your way to twist it. I haven't used the universal hackle pliers in years, they don't even make it in my main tying kit anymore. If you screw it up (unevenly wound) on the rotary, you unwind and wrap it again in two seconds.
But that doesn't answer the question... the bobbin holder pivots on the vise shaft, and tilts on it's own shaft axis too. I swing the holder to the front (away from me) while wrapping stuff, and swing it in when I need it to hold the bobbin.
When do you need to hold the bobbin?
Let's go back to the wolly bugger. After tying in the hackle at the front of the fly, you've completed the chenille body by spinning the fly hook while holding the chenille like a lathe bit. Pc of cake. Now, you tie down the end of the chenille using a whip finish, I prefer the matarelli tool, some prefer their fingers. I can do both but the tool is so much easier for me (results may vary).
Swing the bobbin arm closer so it is in-line with the fly shaft, and lay the thread coming from the whipped chenille (near the bend of the hook) onto the arm. Now you can take your hands off everything and grab the hackle that winds over the chenille. Hold it flat against the chenille and turn the rotary vise, laying the feather on the chenille in a spiral toward the tail as the fly spins. The thread and bobbin are held by the arm and thus does not dangle, twist or wrap during this step... because the thread lies in the same axis as the hook while spinning.
Now that the hackle has been wound to the spot where the thread was whipped in place, you can now pick up the bobbin and wrap the feather in place. even if you preferred to tie in the marabou first, the thread and the marabou would be in-line and spinning with each other so would not tangle during the hackle wrap.
Once again, some tie circles around me with a fixed vise. Your results may vary.
.02
Juro