Interpolation is the computation of values based on neighboring values. It easiest to think of this as the quality level of scaling - or changing the size of an image - but it also affects things like positioning and rotation. It is also called sub-pixel rendering because it gives the impression of positioning between actual pixels.
This settings appears in the Player category of Settings because this only affects preview. There is a separate interpolation option in Export > Advanced > Video.
These names are based on algorithms. You can search for them on Wikipedia to get started on learning more about theme. Shotcut provides hints about the quality and speed trade-offs. Nearest Neighbor actually means no interpolation, no sub-pixel rendering.
This setting does not affect text or SVG anti-aliasing. It also does not apply to HTML.