Power supply 12vac to DC
why does 12v ac became 15v on the output?


Because of this: -



Your AC may be only 12 volts RMS but its peak value will be \$\sqrt2\$ higher at nearly 17 volts. After losing a couple of diode drops in the bridge this will become about 15.6 volts on your smoothing capacitor and, if you have a load connected there might be enough ripple voltage on the DC to give you an average DC value closer to 15 volts. 

Here's some more information about the relationship between average, RMS and peak voltages on an AC waveform: -



The RMS of an AC waveform is equivalent to a DC voltage that heats a one ohm resistor the same amount so, if you wanted to prove that RMS is 0.7071x peak voltage you need to do some maths.