You don't seem to be considering the currents in the primary and secondary. If you connect a resistive 'load', for example an old-fashioned filament lamp, across the secondary, there will be a current through it. There will then also be a (larger) current through the primary in a step-up transformer. To a fair approximation, the mean power supplied to the primary will equal the mean power supplied by the secondary.
But why should these mean powers be equal? At high school level it's usual to tell students that it is because transformers can't dissipate much power internally (the resistances of the primary and secondary are small, and the soft iron core, if laminated, won't carry significant eddy currents). Since energy is conserved and not much of the energy put in becomes random thermal energy in the transformer itself, the electrical power out almost equals the electrical power going in.
This explanation isn't wrong, but it leaves a lot of questions unanswered. For example, currents and voltages are alternating (glossed over in the naïve equation $V_p I_p=V_s I_s$). And as the resistance of the coils is low, why doesn't the primary take a high current from the supply even when the secondary is open circuit? In a full treatment of transformers the variation of magnetic flux in the core and emfs induced in both coils play a major role. It's fairly intricate, university-level stuff.