an unregulated power supply
An unregulated power supply is the simplest way to make DC from the wall: it converts and smooths the mains, but it does nothing to hold the output steady. Think of a rain barrel fed by a roof. You get water, but the level rises in a downpour and sags when many taps are open. The voltage it gives you wobbles with the mains voltage and with how much current you draw — useful, but not trustworthy for fussy circuits.
The classic chain has three parts and no brain. A transformer steps the mains down to a lower AC voltage; a rectifier (often a bridge of four diodes) flips the negative half-cycles up so current always flows one way; and a big reservoir capacitor charges up on each peak and supplies the load between peaks. The output is roughly the transformer's peak voltage minus a couple of diode drops, with a sawtooth ripple riding on top. Example: a 12 V RMS transformer peaks at about 12 times 1.414 = 17 V; subtract roughly 1.4 V for two bridge diodes and the capacitor sits near 15.6 V, sagging a volt or two of ripple under load.
Why it matters: an unregulated supply is cheap, rugged, and quiet (no switching noise), and it is fine for things that do not care about exact voltage — a relay coil, a heater, a motor, or the raw input feeding a regulator. But its output drifts with mains voltage (a 10 percent mains swing becomes a 10 percent output swing), sags as you load it, and carries ripple. Whenever a circuit needs a precise, steady rail — logic, op-amps, references — you follow the unregulated supply with regulation.
A hobby bench supply made from a 12 V transformer, a bridge rectifier, and a 4700 uF capacitor reads about 16 V with no load but droops to 14 V and shows 1 V of ripple when you draw 0.5 A. Plug in more gear and the voltage sags further — exactly the behaviour a regulator is added to cure.
Transformer, rectifier, reservoir cap — DC, but it wanders with mains and load.
Its no-load voltage can be much higher than its rated full-load voltage, because the capacitor charges to the unloaded peak. Size downstream parts (and any regulator's input rating) for that higher voltage, not the nominal one.