Flying east to west up across the Arctic circle follows what is known as a great circle route and thus is a shorter flight distance then heading across the ocean directly. Because of head winds that would be encountered flying West it is faster to fly this great circle route then it would be to go across the ocean and burn more fuel. If the jet you were in flew at (lets say) 500mph, encountered a headwind of 120mph, its ground speed would be 380mph which would add at least a few hours on a long flight like that. Depending on the season, flying this far North would also take you out of some of the jet stream regions and reduce your headwinds even further.
However, on the way back, the aircraft can make use of the wind (in this case now it is a tailwind at 120mph) which will increase your groundspeed and thus make the overall trip shorter. So, the 500mph jet now would be travelling at a groundspeed of 620mph, which from the viewpoint of someone on the ground would be approaching the speed of sound. This would cut off a few hours and make it worth while to head across the ocean instead of following a great circle back.
Making use of a tailwind almost always makes for a shorter flight...
As for is turbulence stronger during these head/tail wind situations, I am not really 100% sure. Turbulence would in theory be more pronounced when you crossed boundries between regions of wind that was moving at different speeds, but I suspect that if you were in a consistenly moving airmass you would would experience very little turbulence.