Why off-line power supplies are called so, like they are "off the line"?
For me, who are not native English speakers, the terminology is a bit mysterious. 
However here I found this definition:


  Off-line power supply: a PSU that processes electric power from AC line without using line frequency transformer. Such supply can still be isolating if it uses high-frequency transformer in one of its power conversion stages. A typical off-line SMPS rectifies input AC line voltage, produces high-frequency pulses by using semiconductor power switches, changes the voltage level by using inductors and/or transformers, then rectifies it again and filters for DC output. An example of isolating off-line PSU is a switching power supply of a computer.