What is transformerless power supply?

Answer 1

One type is a special kind of switching regulated powersupply. It uses a simple rectifier to convert the input AC to DC, then the switching regulator sends very small current pulses to the output filter capacitors to keep them charged to voltages much smaller than the input voltage.

An older type is what is called an AC/DC powersupply, because it could be plugged into either AC powerline voltage or DC powerline voltage. It was originally designed for inexpensive vacuum tube radios in the 1930s, when many parts of the US still had old style 110 VDC Edison power. Radios using this type of powersupply continued to be sold in the US through the 1960s, when transistors eventually made tube based radios obsolete.