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Transformers raise or lower voltage of ac circuits. They also do the opposite to current, e.g. Raise voltage, lower current.
The rectifier makes all the voltage positive (or negative, but all the same). So yes, AC -> DC
The filter basically uses inductors and capacitors to act as storage. Using capacitor as an example, it'll start charging when the wave starts to rise. once the wave goes down, the capacitor discharges which keeps the output more positive. You can see that in the image by full humps before and partial humps after. It's still bumpy, but it never goes to zero.
The regulator can do a couple of things, mostly it's used to ensure a constant output. In it's most basic, it'll be another diode that if voltage goes above a certain threshold, it shunts it away from the load. So if the output of the filter had a minimum of 5 volts and the regulator was set to 5, you'll end up with a constant positive 5 volts because the diode is shunting away all the extra voltage.
Regulators can provide both over and under voltage protection in case there is fluctuations in the circuit.
Thank you!