I know that in a step-down transformer if I have 10 turns on the primary coil and 5 turns on the secondary coil that the voltage gets reduced by half and the current gets doubled, but is there any other significance?
The magnetic flux generated by the current is proportional to the number of turns of the coil.
Often wondered this myself. There must be a reason why you get transformers with 1000 turns on the primary, and 500 turns on the secondary. If there wasn't a good reason why would manufactures bother putting more than 2 turns on the primary and a single turn on the secondary? The ratio remains the same! Think it could be something to do with the impedance the transformer offers to the input, and output circuits. impedance is kind the AC equivalent of resistance. If it's high then there'll be a fair impedance(resistance to the instantaneous flow of current for a given instantaneous voltage. More turnslonger wirehigher impedance? Matching of impedance between circuits can be important to ensure maximum efficiency/preventing echos etc.