Ian, "reins" are the leather bands used to control a horse.
"To hold reins" means to hold power.
So, depending upon the context, "she held the reins in her hands" can mean
1. she held the reins (leather bands) in her hands to control the horse.
2. she held power.
"When the king became ill, he handed over the reins to his son."
In this example, it means, the king passed on the power to his young son.
"The prince had to take up the reins from his father at an early age."
That is, the prince took over power from his father at an early age.
Hope this helps.