Could mean all of the above, depending on the bowler.

For me, it might mean a cocked wrist instead of straight. But usually, my adjustment is more one of feel. If I want more forward roll, I make sure that the ball weight is toward the ball of my hand (think under the index and middle finger), if I want more side roll, I want the weight of the ball to be more toward the side of my hand under the pinky and ring finger. Using this method, I don't really have to change the actual position of my hand, just where the pressure of the ball is located.

Your mileage may vary! 

I just use a small adjustment as to where the weight of the ball is on my hand. I want to keep my hand behind the ball until the release point, but in the stance, I can adjust where I feel the weight of the ball. It's a very subtle change that works well for me. If you watch Norm Duke in his set up, it looks as if he is doing something similar at times.

I have heard many times bowlers say I changed my hand position to accomplish this or that on the lane. My question is what exactly are they talking about? Does it mean coming more up the back of the ball, pinky/index finger in a different position on the ball, wrist cocked/straighter when holding the ball. Thanks

 Yes, burly has exactly the reply I was coming here to share. For me, I have been using a system like this for YEARS, and it allows me much versatility to create different looks while using the same piece of equipment.

 Like milorafferty said, it makes the ball "feel" like it is in a different position in the hand, and changes the way I come through (or around) the ball during the release.