The output voltage is about 1.414 x the secondary voltage,ie. 9 x 1.414 = 12.726volts DC. This is refered to as half wave rectification, because the diode only conducts on the positive half cycle of the secondary output waveform. The purpose of C1 is to "smooth" out the DC and to store
current.
AC = Alternating current
DC = Direct current
L = The live side of the mains supply
N = The neutral side of the mains supply
C = An abreviation for a capacitor