Why IF Shift moves the receiver's IF filter passband up or down relative to the incoming signal while the BFO tracks along with it, so the recovered audio pitch stays the same. By sliding the passband window you can push an interfering heterodyne or an adjacent signal outside the filter skirts while keeping the desired signal inside. It is a selectivity tool: same bandwidth, different placement of that bandwidth.
Watch out Tuning in a station that is slightly off frequency without moving your transmit frequency is what RIT (receiver incremental tuning, or the clarifier) does, and listening on a frequency different from your transmit frequency is split operation, not IF Shift.
IF Shift slides the filter window, not the frequency. Shift = shove the QRM out of the passband.