Why A repeater listens on one frequency (its input) and retransmits on another (its output) at the same time, so the two must be separated far enough that the transmitter does not desense the receiver. That frequency separation is the offset, and your radio applies it automatically when you transmit on a repeater channel. Standard offsets in the US are 600 kHz on 2 meters and 5 MHz on 70 cm, with 1.6 MHz commonly used on 222 MHz.
Watch out The choices about time delays describe other repeater behaviors, such as the courtesy tone or squelch tail you hear after someone unkeys, not the frequency split; offset is about hertz, not seconds.
Offset = frequency shift, not time shift. Remember 600 kHz on 2 m, 5 MHz on 70 cm.