How do step-up transformers exist?
Ignoring the detail that you can't transform the DC output of a battery, you have discovered the fact that a transformer (appears to) transform the impedance. (By the square of the turn ratio, as Olin provided. I recall using  speaker transformers salvaged from tube amplifiers as mains transformers, and vice versa.)

How is a problematic type of question, what kind of answer do you expect? "By obeying the laws of nature" would be the most correct answer.

You could compare a transformer to a pair of gear wheels: when a very strong man tries to turn the big wheel, a feeble child can stop him by holding on to the small wheel. The small resistance (to turning) provided by the child is transformed by the gears to a big resistance as felt by the big man.